{"id":378,"date":"2023-07-04T04:08:40","date_gmt":"2023-07-04T04:08:40","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d8%b9%d8%af%d9%85-%d8%a7%d9%84%d8%aa%d8%ad%d8%af%d9%8a%d8%af-%d9%84%d8%a7-%d9%86%d9%87%d8%a7%d8%a6%d9%8a-%d9%86%d8%a7%d9%82%d8%b5-%d9%84%d8%a7-%d9%86%d9%87%d8%a7%d8%a6%d9%8a-%e2%88%9e-%e2%88%9e\/"},"modified":"2023-07-04T04:08:40","modified_gmt":"2023-07-04T04:08:40","slug":"%d8%b9%d8%af%d9%85-%d8%a7%d9%84%d8%aa%d8%ad%d8%af%d9%8a%d8%af-%d9%84%d8%a7-%d9%86%d9%87%d8%a7%d8%a6%d9%8a-%d9%86%d8%a7%d9%82%d8%b5-%d9%84%d8%a7-%d9%86%d9%87%d8%a7%d8%a6%d9%8a-%e2%88%9e-%e2%88%9e","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d8%b9%d8%af%d9%85-%d8%a7%d9%84%d8%aa%d8%ad%d8%af%d9%8a%d8%af-%d9%84%d8%a7-%d9%86%d9%87%d8%a7%d8%a6%d9%8a-%d9%86%d8%a7%d9%82%d8%b5-%d9%84%d8%a7-%d9%86%d9%87%d8%a7%d8%a6%d9%8a-%e2%88%9e-%e2%88%9e\/","title":{"rendered":"\u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0646\u0627\u0642\u0635 \u0644\u0627\u0646\u0647\u0627\u0626\u064a (\u221e-\u221e)"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0646\u0634\u0631\u062d \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629 \u0643\u064a\u0641\u064a\u0629 \u062d\u0644 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0646\u0627\u0642\u0635 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a (\u221e-\u221e). \u0633\u062a\u062c\u062f \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0647\u0630\u0627 \u0645\u0639 \u0623\u0646\u0648\u0627\u0639 \u0645\u062e\u062a\u0644\u0641\u0629 \u0645\u0646 \u0627\u0644\u0648\u0638\u0627\u0626\u0641\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0645\u0646 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0646\u0627\u0642\u0635 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"resolver-la-indeterminacion-infinito-menos-infinito\"><\/span> \u062d\u0644 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0646\u0627\u0642\u0635 \u0644\u0627\u0646\u0647\u0627\u0626\u064a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0646\u062f\u0645\u0627 \u062a\u0639\u0637\u064a \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629 \u0646\u0627\u0642\u0635 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629\u060c \u0641\u0647\u0630\u0627 \u064a\u0639\u0646\u064a \u0623\u0646\u0647\u0627 \u063a\u064a\u0631 \u0645\u062d\u062f\u062f\u0629 (\u0623\u0648 \u0634\u0643\u0644 \u063a\u064a\u0631 \u0645\u062d\u062f\u062f). \u0648\u0647\u0630\u0627 \u064a\u0639\u0646\u064a <strong>\u0623\u0646 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u064a \u062a\u0639\u0637\u064a \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0646\u0627\u0642\u0635 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629<\/strong> \u0644\u0627 \u064a\u0645\u0643\u0646 \u062a\u062d\u062f\u064a\u062f\u0647\u0627 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0628\u0627\u0634\u0631\u060c \u0628\u0644 \u064a\u062c\u0628 \u062a\u0646\u0641\u064a\u0630 \u0625\u062c\u0631\u0627\u0621 \u0623\u0648\u0644\u064a.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643\u060c \u0644\u062d\u0644 <strong>\u0645\u0634\u0643\u0644\u0629 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0646\u0627\u0642\u0635 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u060c<\/strong> \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0623\u0648\u0644\u0627\u064b \u062a\u0637\u0628\u064a\u0642 \u0625\u062c\u0631\u0627\u0621 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0646\u0648\u0639 \u0627\u0644\u0648\u0638\u064a\u0641\u0629: \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u062f\u0627\u0644\u0629 \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u062d\u062f\u0648\u062f\u060c \u0641\u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628\u0647\u0627 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0627\u0644\u0645\u0642\u0627\u0631\u0646\u0629\u060c \u0648\u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u062f\u0627\u0644\u0629 \u0643\u0633\u0631\u064a\u0629\u060c \u0641\u064a\u062c\u0628 \u0627\u062e\u062a\u0632\u0627\u0644 \u0627\u0644\u0643\u0633\u0648\u0631 \u0625\u0644\u0649 \u0642\u0627\u0633\u0645\u064b\u0627 \u0645\u0634\u062a\u0631\u0643\u064b\u0627\u060c \u0648\u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u062f\u0627\u0644\u0629 \u063a\u064a\u0631 \u0646\u0633\u0628\u064a\u0629 \u0641\u064a\u062c\u0628 \u0636\u0631\u0628\u0647\u0627 \u0628\u0627\u0644\u0645\u0631\u0627\u0641\u0642.<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b1bfc56d2079c86e8ad6e1943311b730_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to+\\infty}\\Bigl(f(x)-g(x)\\Bigr)=\\infty-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"236\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0639\u062f \u0630\u0644\u0643\u060c \u0633\u0646\u0631\u0649 \u0628\u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0643\u064a\u0641 \u064a\u062a\u0645 \u062d\u0644 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0646\u0627\u0642\u0635 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0641\u064a \u0643\u0644 \u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0648\u0638\u0627\u0626\u0641. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"indeterminacion-infinito-menos-infinito-en-funciones-polinomicas\"><\/span> \u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0646\u0627\u0642\u0635 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0641\u064a \u0648\u0638\u0627\u0626\u0641 \u0643\u062b\u064a\u0631\u0629 \u0627\u0644\u062d\u062f\u0648\u062f <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div style=\"background:linear-gradient(to bottom, #FFFFFF 0%, #FFE0B2 100%); padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px; margin-bottom:30px;text-align:right;direction:rtl\">\n<p style=\"text-align:left;text-align:right;direction:rtl\"> \u0641\u064a \u0643\u062b\u064a\u0631\u0629 \u0627\u0644\u062d\u062f\u0648\u062f\u060c \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0646\u0627\u0642\u0635 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u062a\u0633\u0627\u0648\u064a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u0631\u062a\u0628\u0629 \u0627\u0644\u0623\u0639\u0644\u0649\u060c \u0623\u064a \u0623\u0646 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0639\u0644\u0649 \u064a\u062d\u062f\u062f \u0627\u0644\u0625\u0634\u0627\u0631\u0629 \u0627\u0644\u0625\u064a\u062c\u0627\u0628\u064a\u0629 \u0623\u0648 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 \u0644\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629.<\/p>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0627\u0646\u0638\u0631 \u0625\u0644\u0649 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0648\u0627\u0644\u062a\u064a \u062a\u0639\u0637\u064a \u0627\u0644\u0635\u064a\u063a\u0629 \u063a\u064a\u0631 \u0627\u0644\u0645\u062d\u062f\u062f\u0629 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629 \u0646\u0627\u0642\u0635 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f61115731d29dc9f05941968417c9443_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to+\\infty}\\bigl(x^2-3x\\bigr)=(+\\infty)^2-3\\cdot (\\infty)=+\\infty-\\infty=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"421\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u0627\u0644\u062d\u062f x <sup>2<\/sup> \u0647\u0648 \u0645\u0646 \u0627\u0644\u062f\u0631\u062c\u0629 \u0627\u0644\u062b\u0627\u0646\u064a\u0629 \u0648\u0627\u0644\u062d\u062f 3x \u0647\u0648 \u0645\u0646 \u0627\u0644\u062f\u0631\u062c\u0629 \u0627\u0644\u0623\u0648\u0644\u0649\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0623\u062d\u0627\u062f\u064a\u0629 \u0627\u0644\u062d\u062f x <sup>2<\/sup> \u0647\u064a \u0627\u0644\u0645\u0647\u064a\u0645\u0646\u0629 \u0644\u0623\u0646\u0647\u0627 \u0630\u0627\u062a \u0631\u062a\u0628\u0629 \u0623\u0639\u0644\u0649. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0647\u064a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0645\u0646 \u0647\u0630\u0627 \u0627\u0644\u062d\u062f.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0644\u0642\u0650 \u0646\u0638\u0631\u0629 \u0639\u0644\u0649 \u0647\u0630\u0647 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0627\u0644\u0623\u062e\u0631\u0649:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3bfb5cd294a19de382f74738af6be724_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x\\to+\\infty}\\bigl(x^5-4x^2-3x\\bigr)=(+\\infty)^5=+\\infty\\\\[5ex]\\displaystyle\\lim_{x\\to-\\infty}\\bigl(-3x^2-5x\\bigr)=-3\\cdot (-\\infty)^2=-3\\cdot \\infty=-\\infty\\\\[5ex]\\displaystyle\\lim_{x\\to+\\infty}\\bigl(x^7-5x^4+x^3-2x-10\\bigr)=(+\\infty)^7=+\\infty\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"150\" width=\"387\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0627\u062e\u062a\u0635\u0627\u0631\u060c \u0639\u0646\u062f\u0645\u0627 \u0646\u0636\u0639 \u062d\u062f\u0648\u062f\u064b\u0627 \u0644\u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629 \u0641\u064a \u062f\u0648\u0627\u0644 \u0643\u062b\u064a\u0631\u0629 \u0627\u0644\u062d\u062f\u0648\u062f <strong>\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0628\u0628\u0633\u0627\u0637\u0629 \u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629 \u0641\u064a \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0639\u0644\u0649 \u062f\u0631\u062c\u0629<\/strong> \u060c \u0645\u062a\u062c\u0627\u0647\u0644\u064a\u0646 \u062c\u0645\u064a\u0639 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0623\u062e\u0631\u0649. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"indeterminacion-infinito-menos-infinito-con-fracciones\"><\/span> \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0646\u0627\u0642\u0635 \u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0645\u0639 \u0627\u0644\u0643\u0633\u0648\u0631 <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div style=\"background:linear-gradient(to bottom, #FFFFFF 0%, #FFE0B2 100%); padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px; margin-bottom:30px;text-align:right;direction:rtl\">\n<p style=\"text-align:left;text-align:right;direction:rtl\"> \u0639\u0646\u062f\u0645\u0627 <strong>\u062a\u062d\u062f\u062b \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0646\u0627\u0642\u0635 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0641\u064a \u0639\u0645\u0644\u064a\u0629 \u062c\u0645\u0639 \u0623\u0648 \u0637\u0631\u062d \u0627\u0644\u0643\u0633\u0648\u0631 \u0627\u0644\u062c\u0628\u0631\u064a\u0629<\/strong> \u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0623\u0648\u0644\u0627\u064b \u0625\u062c\u0631\u0627\u0621 \u0639\u0645\u0644\u064a\u0629 \u062c\u0645\u0639 \u0623\u0648 \u0637\u0631\u062d \u0627\u0644\u0643\u0633\u0648\u0631 \u062b\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629.<\/p>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u062f\u0639\u0648\u0646\u0627 \u0646\u0631\u0649 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0646\u0627\u0642\u0635 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0641\u064a \u062f\u0627\u0644\u0629 \u062a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0643\u0633\u0648\u0631 \u0639\u0646 \u0637\u0631\u064a\u0642 \u062d\u0644 \u0645\u062b\u0627\u0644 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c58eb86af2eb0393a802fc7a29f8a453_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\left( \\frac{x^2}{x-1} - \\frac{x}{3}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"152\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062f\u0639\u0648\u0646\u0627 \u0646\u062d\u0627\u0648\u0644 \u062d\u0633\u0627\u0628 \u0627\u0644\u062d\u062f \u0623\u0648\u0644\u0627\u064b:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b3a2cbbfec28f9de05668b90e9ee65f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty}\\left(  \\frac{x^2}{x-1} - \\frac{x}{3}\\right) = \\frac{(+\\infty)^2}{(+\\infty)-1} - \\frac{+\\infty}{3} = \\bm{+\\infty - \\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"410\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0643\u0646\u0646\u0627 \u062d\u0635\u0644\u0646\u0627 \u0639\u0644\u0649 \u0639\u062f\u0645 \u0627\u0644\u062a\u0639\u064a\u064a\u0646 \u221e-\u221e.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0627 \u0639\u0644\u064a\u0646\u0627 \u0623\u0648\u0644\u064b\u0627 \u0623\u0646 \u0646\u0642\u0648\u0645 \u0628\u0637\u0631\u062d \u0627\u0644\u0643\u0633\u0648\u0631. \u0644\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643\u060c \u0646\u0642\u0648\u0645 \u0628\u062a\u0642\u0644\u064a\u0644 \u0627\u0644\u0643\u0633\u0648\u0631 \u0625\u0644\u0649 \u0645\u0642\u0627\u0645 \u0645\u0634\u062a\u0631\u0643\u060c \u0623\u064a \u0623\u0646\u0646\u0627 \u0646\u0636\u0631\u0628 \u0628\u0633\u0637 \u0648\u0645\u0642\u0627\u0645 \u0643\u0633\u0631 \u0648\u0627\u062d\u062f \u0641\u064a \u0645\u0642\u0627\u0645 \u0627\u0644\u0622\u062e\u0631:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-68e489c5833478cb20929ea07ae2971d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x \\to +\\infty} \\left( \\frac{x^2}{x-1}-\\frac{x}{3}\\right)=\\\\[5ex]\\displaystyle =\\lim_{x \\to +\\infty}\\left(\\frac{x^2 \\cdot 3}{(x-1)\\cdot 3}- \\frac{x\\cdot (x-1)}{3\\cdot (x-1)} \\right)=\\\\[5ex]\\displaystyle = \\lim_{x \\to +\\infty} \\left( \\frac{3x^2 }{3(x-1)}- \\frac{x^2-x}{3(x-1)}\\right)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"188\" width=\"295\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0627\u0644\u0622\u0646 \u0628\u0639\u062f \u0623\u0646 \u0623\u0635\u0628\u062d \u0644\u0643\u0644\u0627 \u0627\u0644\u0643\u0633\u0631\u064a\u0646 \u0646\u0641\u0633 \u0627\u0644\u0645\u0642\u0627\u0645\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u062f\u0645\u062c\u0647\u0645\u0627 \u0641\u064a \u0643\u0633\u0631 \u0648\u0627\u062d\u062f:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1e5345a6d68ae0cdda543b81f89daa62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\frac{3x^2 -(x^2-x)}{3(x-1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"163\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0646 \u0646\u0639\u0645\u0644 \u0641\u064a \u0627\u0644\u0628\u0633\u0637 \u0648\u0627\u0644\u0645\u0642\u0627\u0645:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-31cbae0091a641d74250fae5758b3116_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty}  \\frac{3x^2 -x^2+x}{3x-3} =  \\lim_{x \\to +\\infty}  \\frac{2x^2+x}{3x-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"284\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u062d\u0633\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0645\u0631\u0629 \u0623\u062e\u0631\u0649:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6ef29c026035a5353b2bada5bc0d9ff9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty}\\frac{2x^2+x}{3x-3}=\\frac{+\\infty}{+\\infty}=\\bm{+\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"225\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u0641\u0625\u0646 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0628\u064a\u0646 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u064a\u0639\u0637\u064a +\u221e \u0644\u0623\u0646 \u062f\u0631\u062c\u0629 \u0627\u0644\u0628\u0633\u0637 \u0623\u0643\u0628\u0631 \u0645\u0646 \u062f\u0631\u062c\u0629 \u0627\u0644\u0645\u0642\u0627\u0645.<\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0627\u0646\u0638\u0631:<\/strong> <a href=\"https:\/\/mathority.org\/ar\/\u0639\u062f\u0645-\u0627\u0644\u062a\u062d\u062f\u064a\u062f-\u0644\u0627\u0646\u0647\u0627\u064a\u0654\u064a-\u0628\u064a\u0646-\u0644\u0627\u0646\u0647\u0627\u064a\u0654\u064a-%e2%88%9e-%e2%88%9e\/\"><span style=\"text-decoration: underline;\">\u0645\u0627 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629\u061f<\/span><\/a> <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"indeterminacion-infinito-menos-infinito-con-raices\"><\/span> \u0639\u062f\u0645 \u0627\u0644\u062a\u0639\u064a\u064a\u0646 \u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0646\u0627\u0642\u0635 \u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0645\u0639 \u0627\u0644\u062c\u0630\u0648\u0631 <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div style=\"background:linear-gradient(to bottom, #FFFFFF 0%, #FFE0B2 100%); padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px; margin-bottom:30px;text-align:right;direction:rtl\">\n<p style=\"text-align:left;text-align:right;direction:rtl\"> \u0639\u0646\u062f\u0645\u0627 <strong>\u062a\u062d\u062f\u062b \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0646\u0627\u0642\u0635 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0641\u064a \u0627\u0644\u062c\u0645\u0639 \u0627\u0644\u062c\u0630\u0631\u064a \u0623\u0648 \u0627\u0644\u0637\u0631\u062d<\/strong> \u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0623\u0648\u0644\u0627\u064b \u0636\u0631\u0628 \u0627\u0644\u062f\u0627\u0644\u0629 \u0648\u062a\u0642\u0633\u064a\u0645\u0647\u0627 \u0628\u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062c\u0630\u0631\u064a \u0627\u0644\u0645\u062a\u0631\u0627\u0641\u0642\u060c \u062b\u0645 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0646\u0647\u0627\u064a\u0629.<\/p>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0633\u0646\u0631\u0649 \u0643\u064a\u0641\u064a\u0629 \u062d\u0644 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0646\u0627\u0642\u0635 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0641\u064a \u062f\u0627\u0644\u0629 \u063a\u064a\u0631 \u0639\u0642\u0644\u0627\u0646\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u062b\u0627\u0644 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e093b62c357684fe8a8818df58d7b99a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\left(x-\\sqrt{x^2-5}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"165\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062f\u0639\u0648\u0646\u0627 \u0646\u062d\u0627\u0648\u0644 \u0623\u0648\u0644\u0627\u064b \u062d\u0644 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062c\u0630\u0648\u0631:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4459c2b6c968344878499cfbb30adda4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\left(x-\\sqrt{x^2-5}\\right)=+\\infty-\\sqrt{(+\\infty)^2}=\\bm{+\\infty-\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"409\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u062d\u0635\u0644\u0646\u0627 \u0639\u0644\u0649 \u0627\u0644\u0635\u064a\u063a\u0629 \u063a\u064a\u0631 \u0627\u0644\u0645\u062d\u062f\u062f\u0629 \u221e-\u221e. \u0644\u0630\u0627\u060c \u0644\u0645\u0639\u0631\u0641\u0629 \u0645\u0642\u062f\u0627\u0631 \u0639\u062f\u0645 \u0627\u0644\u062a\u0639\u064a\u064a\u0646 \u0627\u0644\u0630\u064a \u064a\u0633\u0627\u0648\u064a \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629 \u0646\u0627\u0642\u0635 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629\u060c \u0639\u0644\u064a\u0646\u0627 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u0645\u0648\u0636\u062d.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0645\u0627 \u0623\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0647\u0627 \u062c\u0630\u0648\u0631\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u0636\u0631\u0628 \u0627\u0644\u062f\u0627\u0644\u0629 \u0628\u0623\u0643\u0645\u0644\u0647\u0627 \u0648\u0646\u0642\u0633\u0645\u0647\u0627 \u0628\u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u063a\u064a\u0631 \u0627\u0644\u0639\u0642\u0644\u0627\u0646\u064a \u0627\u0644\u0645\u0642\u062a\u0631\u0646:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f10d91882a0f8dcca86fbb8dda7da7cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to +\\infty}\\left(x-\\sqrt{x^2-5}\\right)= \\lim_{x \\to +\\infty}\\frac{\\left(x-\\sqrt{x^2-5}\\right)\\cdot\\left(x+\\sqrt{x^2-5}\\right)}{x+\\sqrt{x^2-5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"488\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u062a\u0648\u0627\u0641\u0642 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062c\u0628\u0631\u064a \u0644\u0644\u0628\u0633\u0637 \u0645\u0639 \u0627\u0644\u0647\u0648\u064a\u0629 \u0627\u0644\u0628\u0627\u0631\u0632\u0629 \u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0645\u062c\u0645\u0648\u0639 \u0628\u0641\u0627\u0631\u0642\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u0628\u0633\u064a\u0637 \u0627\u0644\u062a\u0639\u0628\u064a\u0631:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b00f177bdb579dabf9dc589e387344cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{\\left(x-\\sqrt{x^2-5}\\right) \\cdot \\left(x + \\sqrt{x^2-5}\\right)}{ x + \\sqrt{x^2-5}}= \\lim_{x \\to +\\infty} \\cfrac{x^2- \\left( \\sqrt{x^2-5}\\right)^2}{ x + \\sqrt{x^2-5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"505\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u0642\u0648\u0645 \u0627\u0644\u0622\u0646 \u0628\u062a\u0628\u0633\u064a\u0637 \u062c\u0630\u0631 \u0627\u0644\u0646\u0647\u0627\u064a\u0629\u060c \u062d\u064a\u062b \u0625\u0646\u0647\u0627 \u0645\u0631\u0628\u0639\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d5c798f099ef1c56a50526e7fba8c99c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty}\\frac{x^2-(x^2-5)}{x+\\sqrt{x^2-5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"153\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0646 \u0646\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0628\u0633\u0637 \u0627\u0644\u0643\u0633\u0631:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-392ae211b16ad803eb70cc4993a0c7e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\frac{x^2- x^2+5}{x+\\sqrt{x^2-5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"146\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-be954eaf609b9f98c6dc984758599b5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\frac{5}{x+\\sqrt{x^2-5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"146\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u0639\u064a\u062f \u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c29edfa5eba2fe54e369c3d963d11a45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\frac{5}{x+\\sqrt{x^2-5}}=\\frac{5}{+\\infty+\\sqrt{(+\\infty)^2}}=\\frac{5}{+\\infty}=\\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"391\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0647\u064a 0\u060c \u0644\u0623\u0646 \u0623\u064a \u0639\u062f\u062f \u0645\u0642\u0633\u0648\u0645 \u0639\u0644\u0649 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629 \u064a\u0633\u0627\u0648\u064a \u0635\u0641\u0631\u064b\u0627. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-indeterminacion-infinito-menos-infinito\"><\/span> \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0646\u0627\u0642\u0635 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 1<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u0644 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0645\u0639 \u0627\u0642\u062a\u0631\u0627\u0628 x \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bac36c53d4e34c6e9972009b34a64c21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}(7x^2-2x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"134\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u062d\u062f \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0639\u0644\u0649 \u0647\u0648 \u0645\u0646 \u0627\u0644\u062f\u0631\u062c\u0629 \u0627\u0644\u062b\u0627\u0644\u062b\u0629\u060c \u0644\u0630\u0644\u0643 \u0646\u0631\u0643\u0632 \u0639\u0644\u0649 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0645\u062a\u062d\u0635\u0644 \u0639\u0644\u064a\u0647\u0627 \u0645\u0646 \u0647\u0630\u0627 \u0627\u0644\u062d\u062f. <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eee2b50312f5fd4225c85387c311eec5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}(+7x^2-2x^3)=+\\infty^2-\\infty^3=+\\infty-\\infty=\\bm{-\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"408\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u062a\u0645\u0631\u064a\u0646 2<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u062d\u0633\u0628 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 \u062a\u0642\u062a\u0631\u0628 x \u0645\u0646 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0633\u0627\u0644\u0628\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-12b903d03d726c28b625fe3f5ba4b3c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to -\\infty}(-5x^3-9x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"148\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0633\u0627\u0644\u0628 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0645\u0643\u0639\u0628 \u064a\u0638\u0644 \u0633\u0627\u0644\u0628\u064b\u0627\u060c \u0644\u0643\u0646 \u0639\u0646\u062f \u062a\u0631\u0628\u064a\u0639\u0647 \u064a\u0635\u0628\u062d \u0645\u0648\u062c\u0628\u064b\u0627. \u0644\u0627\u062d\u0642\u0627\u064b \u0645\u0639 \u0623\u0646 \u0625\u0634\u0627\u0631\u0627\u062a\u0647\u0645 \u0645\u0639\u062f\u0644\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u062a\u064a \u0623\u0645\u0627\u0645\u0647\u0645:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-172f2927f65e61079b13abd02234f1c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x\\to -\\infty}(-5x^3+x^2)=\\\\[3ex]=-5(-\\infty)^3-9(-\\infty)^2=\\\\[3ex]=-5\\cdot (-\\infty)-9\\cdot \\infty=\\\\[3ex]=+\\infty-\\infty\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"153\" width=\"196\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0628\u0639\u062f \u0630\u0644\u0643\u060c \u064a\u062a\u0645 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0635\u064a\u063a\u0629 \u063a\u064a\u0631 \u0627\u0644\u0645\u062d\u062f\u062f\u0629 \u0645\u0646 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0646\u0627\u0642\u0635 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0628\u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0639\u0644\u0649 (-5x <sup>3<\/sup> )\u060c \u0648\u0627\u0644\u0630\u064a \u0646\u062d\u0635\u0644 \u0645\u0646\u0647 \u0639\u0644\u0649 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0625\u064a\u062c\u0627\u0628\u064a\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dfd806b31a588234442f48fa5ae8b751_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to -\\infty}(-5x^3+x^2)=\\bm{+\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"194\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u0627\u0644\u062a\u0645\u0631\u064a\u0646 3<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u062f\u062f \u0646\u0647\u0627\u064a\u0629 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0639\u0642\u0644\u0627\u0646\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f0a8401379d90875626b1fbd3714fd01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\left(\\frac{x^3+1}{x-1}-\\frac{x}{4} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"160\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0623\u0648\u0644\u064b\u0627\u060c \u0646\u062d\u0627\u0648\u0644 \u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u0627\u0644\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-43df032007d76e00f2f7366e05f9e697_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\left(\\frac{x^3+1}{x-1}-\\frac{x}{4}\\right)=\\frac{(+\\infty)^3+1}{+\\infty-1}-\\frac{+\\infty}{4} = \\bm{+\\infty -\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"425\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0643\u0646 \u0627\u0646\u062a\u0647\u0649 \u0628\u0646\u0627 \u0627\u0644\u0623\u0645\u0631 \u0625\u0644\u0649 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u221e \u2013 \u221e. \u0648\u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u062e\u062a\u0635\u0631 \u0627\u0644\u0643\u0633\u0648\u0631 \u0625\u0644\u0649 \u0642\u0627\u0633\u0645 \u0645\u0634\u062a\u0631\u0643:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7e2820674bc86d085f6deec7fdf9adf8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim\\limits_{x \\to +\\infty} \\left(\\frac{x^3+1}{x-1}-\\frac{x}{4} \\right)=\\\\[5ex]\\displaystyle = \\lim_{x\\to +\\infty}\\left(\\frac{(x^3+1)\\cdot4}{(x-1)\\cdot4}-\\frac{x\\cdot(x-1)}{4\\cdot (x-1)}\\right)=\\\\[5ex]\\displaystyle =\\lim_{x\\to +\\infty}\\left(\\frac{4x^3+4}{4x-4}-\\frac{x^2-x}{4x-4}\\right)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"188\" width=\"302\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0645\u0627 \u0623\u0646 \u0643\u0644\u0627 \u0627\u0644\u0643\u0633\u0631\u064a\u0646 \u0644\u0647\u0645\u0627 \u0627\u0644\u0622\u0646 \u0646\u0641\u0633 \u0627\u0644\u0645\u0642\u0627\u0645\u060c \u0641\u064a\u0645\u0643\u0646\u0646\u0627 \u062f\u0645\u062c\u0647\u0645\u0627 \u0641\u064a \u0643\u0633\u0631 \u0648\u0627\u062d\u062f:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-93a00027be74b1e60c7ee8537ebe5d9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to +\\infty}\\left(\\frac{4x^3+4}{4x-4}-\\frac{x^2-x}{4x-4}\\right)=\\lim_{x\\to +\\infty}\\frac{4x^3+4-(x^2-x)}{4x-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"429\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0642\u0648\u0645 \u0628\u0639\u0645\u0644 \u0642\u0648\u0633\u064a\u0646 \u0644\u0644\u0628\u0633\u0637:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c7de3ead5b3a5f8bd2ae8d767da693b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to +\\infty} \\frac{4x^3+4-x^2+x}{4x-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"180\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627 \u0646\u062d\u062f\u062f \u0627\u0644\u062d\u062f:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7ffb73fbf26fd2b625e43872a9c10ef9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to +\\infty}\\frac{4x^3+4-x^2+x}{4x-4}=\\frac{4(+\\infty)^3}{4(+\\infty)}=\\frac{+\\infty}{+\\infty} = \\bm{+\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"384\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u221e\/\u221e \u064a\u0639\u0637\u064a +\u221e \u0644\u0623\u0646 \u062f\u0631\u062c\u0629 \u0627\u0644\u0628\u0633\u0637 \u0623\u0643\u0628\u0631 \u0645\u0646 \u062f\u0631\u062c\u0629 \u0627\u0644\u0645\u0642\u0627\u0645.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 4<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u0644 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0643\u0633\u0631\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 \u062a\u0642\u062a\u0631\u0628 x \u0645\u0646 0: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e783bc22baa422d4b537fae4628fb4a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0}\\left(\\frac{-3x-2}{x^4}-\\frac{5}{x^2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"165\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0627\u0648\u0644 \u0623\u0648\u0644\u0627\u064b \u062d\u0633\u0627\u0628 \u0627\u0644\u062d\u062f \u0643\u0627\u0644\u0645\u0639\u062a\u0627\u062f:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-207bc08385f430f0f8c49ac34a10f811_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 0}\\left(\\frac{-3x-2}{x^4}-\\frac{5}{x^2}\\right)=\\frac{-3\\cdot0-2}{0^4}-\\frac{5}{0^2}=\\frac{-2}{0}-\\frac{5}{0}=\\bm{\\infty-\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"477\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0643\u0646\u0646\u0627 \u062d\u0635\u0644\u0646\u0627 \u0639\u0644\u0649 \u0627\u0644\u0635\u064a\u063a\u0629 \u063a\u064a\u0631 \u0627\u0644\u0645\u062d\u062f\u062f\u0629 \u221e-\u221e. \u0648\u0644\u0630\u0644\u0643\u060c \u0639\u0644\u064a\u0646\u0627 \u0627\u062e\u062a\u0632\u0627\u0644 \u0643\u0633\u0648\u0631 \u0627\u0644\u062f\u0627\u0644\u0629 \u0625\u0644\u0649 \u0645\u0642\u0627\u0645 \u0645\u0634\u062a\u0631\u0643.<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c x <sup>4<\/sup> \u0647\u0648 \u0645\u0636\u0627\u0639\u0641 \u0644\u0640 x <sup>2<\/sup> \u060c \u0644\u0630\u0644\u0643 \u0628\u0628\u0633\u0627\u0637\u0629 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0636\u0631\u0628 \u0628\u0633\u0637 \u0648\u0645\u0642\u0627\u0645 \u0627\u0644\u0643\u0633\u0631 \u0627\u0644\u062b\u0627\u0646\u064a \u0641\u064a x <sup>2<\/sup> \u0633\u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0623\u0646 \u0643\u0644\u0627 \u0627\u0644\u0643\u0633\u0631\u064a\u0646 \u0644\u0647\u0645\u0627 \u0646\u0641\u0633 \u0627\u0644\u0645\u0642\u0627\u0645:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-876115dc1fb49e81373d70be5fdcfb5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x \\to 0}\\left(\\frac{-3x-2}{x^4}-\\frac{5}{x^2}\\right)=\\\\[5ex]\\displaystyle =\\lim_{x \\to 0}\\left(\\frac{-3x-2}{x^4}-\\frac{5\\cdot x^2}{x^2\\cdot x^2} \\right)=\\\\[5ex]\\displaystyle =\\lim_{x\\to 0}\\left(\\frac{-3x-2}{x^4}-\\frac{5x^2}{x^4}\\right)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"186\" width=\"235\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u0622\u0646 \u0637\u0631\u062d \u0627\u0644\u0643\u0633\u0631\u064a\u0646:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bf56e81e075d9ac498e9df87a94a675f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 0}\\left(\\frac{-3x-2}{x^4}-\\frac{5x^2}{x^4}\\right)=\\lim_{x\\to 0}\\frac{-3x-2-5x^2 }{x^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"346\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0627\u0648\u0644 \u062d\u0644 \u0627\u0644\u062d\u062f \u0645\u0631\u0629 \u0623\u062e\u0631\u0649:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b231cf80ccb03d1287c1aab47769bc34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 0}  \\cfrac{-3x-2-5x^2 }{x^4} =\\cfrac{-3\\cdot 0-2-5\\cdot 0^2}{0^4}=\\frac{-2}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"370\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0643\u0646 \u0627\u0646\u062a\u0647\u0649 \u0628\u0646\u0627 \u0627\u0644\u0623\u0645\u0631 \u0625\u0644\u0649 \u0639\u062f\u0645 \u062a\u0639\u064a\u064a\u0646 \u0627\u0644\u062b\u0627\u0628\u062a \u0645\u0642\u0633\u0648\u0645\u064b\u0627 \u0639\u0644\u0649 \u0635\u0641\u0631. \u0644\u0630\u0644\u0643 \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u062d\u0633\u0627\u0628 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629. <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c4ced459b1e0da92f03d9d9515b6ea68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 0^{-}} \\frac{-3x-2-5x^2}{x^4}=\\frac{-2}{+0}=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"262\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-239f065e0fe7bb4055e63a8477c030f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 0^{+}}\\frac{-3x-2-5x^2}{x^4}=\\frac{-2}{+0}=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"262\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0627\u0644\u062e\u062a\u0627\u0645\u060c \u0628\u0645\u0627 \u0623\u0646 \u0627\u0644\u0646\u0647\u0627\u064a\u062a\u064a\u0646 \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u062a\u064a\u0646 \u0644\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 x=0 \u062a\u0639\u0637\u064a\u0627\u0646 -\u221e\u060c \u0641\u0625\u0646 \u062d\u0644 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0647\u0648 -\u221e: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-30ab5fa39e1b25568d55de0cc4267dc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 0^-}f(x)=\\lim_{x \\to 0^+}f(x)=-\\infty\\ \\longrightarrow \\  \\lim_{x \\to 0}f(x)= \\bm{-\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"401\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u0627\u0644\u062a\u0645\u0631\u064a\u0646 5<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u0644 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0625\u0644\u0649 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0645\u0639 \u0627\u0644\u062c\u0630\u0648\u0631: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5fb2be8c217ffddadf1b3d9d55f100c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\left(4x^2-\\sqrt{x^4+1}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"182\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0645\u062d\u0627\u0648\u0644\u0629 \u0644\u062d\u0644 \u0627\u0644\u0646\u0647\u0627\u064a\u0629\u060c \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0639\u062f\u0645 \u0627\u0644\u062a\u0639\u064a\u064a\u0646 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0646\u0627\u0642\u0635 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8a1a6b3ff08a703378b8cfb1b5e6532c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\left(4x^2-\\sqrt{x^4+1}\\right)=4(+\\infty)^2-\\sqrt{(+\\infty)^4}=\\bm{+\\infty -\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"456\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643\u060c \u0646\u0638\u0631\u064b\u0627 \u0644\u0648\u062c\u0648\u062f \u062c\u0630\u0648\u0631 \u0641\u064a \u0627\u0644\u062f\u0627\u0644\u0629\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0636\u0631\u0628\u0647\u0627 \u0648\u062a\u0642\u0633\u064a\u0645\u0647\u0627 \u0628\u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062c\u0630\u0631\u064a \u0627\u0644\u0645\u062a\u0631\u0627\u0641\u0642:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3c4cdc9585a792800b8c903745ecc7c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to +\\infty}\\left(4x^2-\\sqrt{x^4+1} \\right)=\\lim_{x \\to +\\infty}\\frac{\\left(4x^2-\\sqrt{x^4+1}\\right)\\cdot\\left(4x^2+\\sqrt{x^4+1}\\right)}{4x^2+\\sqrt{x^4+1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"538\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0627\u0644\u0628\u0633\u0637\u060c \u0644\u062f\u064a\u0646\u0627 \u0627\u0644\u0646\u0627\u062a\u062c \u0627\u0644\u0645\u0644\u062d\u0648\u0638 \u0644\u0644\u0645\u062c\u0645\u0648\u0639 \u0641\u064a \u0627\u0644\u0641\u0631\u0642\u060c \u0648\u0647\u0648 \u0645\u0627 \u064a\u0633\u0627\u0648\u064a \u0627\u0644\u0641\u0631\u0642 \u0628\u064a\u0646 \u0627\u0644\u0645\u0631\u0628\u0639\u064a\u0646. \u062d\u062a\u0649 \u0627\u0644\u0622\u0646:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1aab32f1a28189a4ce96f3816f11a02e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\frac{\\left(4x^2\\right)^2-\\left(\\sqrt{x^4+1}\\right)^2}{4x^2+\\sqrt{x^4+1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"216\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0646 \u0646\u0628\u0633\u0637 \u0627\u0644\u062c\u0630\u0631 \u0625\u0644\u0649 \u0627\u0644\u0645\u0631\u0628\u0639:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6d86adc198c4fb2cd1d99c94e5b8430e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\frac{\\bigl(4x^2\\bigr)^2-(x^4+1)}{4x^2+\\sqrt{x^4+1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"186\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0646 \u0646\u0639\u0645\u0644 \u0641\u064a \u0627\u0644\u0628\u0633\u0637: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c07c403048b4d3e40a8034333ff069c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\frac{16x^4-x^4-1}{4x^2+\\sqrt{x^4+1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"163\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c138b064a8fa3142cb2d50782807ebb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\frac{15x^4-1}{4x^2+\\sqrt{x^4+1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"163\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627 \u0646\u062c\u062f \u0627\u0644\u062d\u062f:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cdb8845be6c640f0370961c3a52598d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\frac{15x^4-1}{4x^2+\\sqrt{x^4+1}}=\\frac{15(+\\infty)^4}{4(+\\infty)^2+\\sqrt{(+\\infty)^4}}=\\frac{+\\infty}{+\\infty}= \\bm{+\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"460\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u064a\u0643\u0648\u0646 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0645\u0642\u0633\u0648\u0645\u064b\u0627 \u0639\u0644\u0649 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0623\u0643\u062b\u0631 \u0644\u0627\u0646\u0647\u0627\u0626\u064a\u064b\u0627 \u0644\u0623\u0646 \u062f\u0631\u062c\u0629 \u0627\u0644\u0628\u0633\u0637 \u0623\u0643\u0628\u0631 \u0645\u0646 \u062f\u0631\u062c\u0629 \u0627\u0644\u0645\u0642\u0627\u0645 (\u062a\u0630\u0643\u0631 \u0623\u0646 \u0627\u0644\u062c\u0630\u0631 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a \u064a\u0642\u0644\u0644 \u0627\u0644\u062f\u0631\u062c\u0629 \u0628\u0645\u0642\u062f\u0627\u0631 \u0627\u062b\u0646\u064a\u0646:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ded55d5413ed7bccc29e8228df205f19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{x^4} = x^{4\/2} = x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"127\" style=\"vertical-align: -1px;\"><\/p>\n<p> ).<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 6<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u0644 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 \u062a\u0642\u062a\u0631\u0628 x \u0645\u0646 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629 \u063a\u064a\u0631 \u0627\u0644\u0645\u0646\u0637\u0642\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7d9f21f0159778cdb1f0710e1a9e0023_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\left(2x-1-\\sqrt{4x^2+1}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"214\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0623\u0648\u0644\u0627\u064b\u060c \u0646\u062d\u0627\u0648\u0644 \u062d\u0633\u0627\u0628 \u0627\u0644\u062d\u062f \u0643\u0627\u0644\u0645\u0639\u062a\u0627\u062f:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5419056e772f9d11884cae7e315ca947_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\left(2x-1-\\sqrt{4x^2+1}\\right)=2(+\\infty)-\\sqrt{4(+\\infty)^2}=\\bm{+\\infty -\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"489\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0643\u0646\u0647 \u064a\u0639\u0637\u064a\u0646\u0627 \u0646\u062a\u064a\u062c\u0629 \u0644\u0630\u0644\u0643 \u0639\u062f\u0645 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0641\u0631\u0642 \u0628\u064a\u0646 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629. \u0644\u0630\u0644\u0643\u060c \u0628\u0645\u0627 \u0623\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0647\u0627 \u062c\u0630\u0648\u0631\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0636\u0631\u0628 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0648\u062a\u0642\u0633\u064a\u0645\u0647 \u0639\u0644\u0649 \u0627\u0644\u062c\u0630\u0631 \u0627\u0644\u0645\u062a\u0631\u0627\u0641\u0642:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bde8a1f86cf7be80170b9595b5a822df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\frac{\\left(2x-1-\\sqrt{4x^2+1}\\right)\\cdot\\left(2x-1+\\sqrt{4x^2+1}\\right)}{2x-1 +\\sqrt{4x^2+1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"393\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0642\u0648\u0645 \u0628\u062a\u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u0633\u0627\u0648\u0627\u0629 \u0627\u0644\u0645\u0644\u062d\u0648\u0638\u0629 \u0644\u0628\u0633\u0637 \u0627\u0644\u0643\u0633\u0631:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e074e8c7841e0951ae03d6dfd2bfd1b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\frac{\\left(2x-1\\right)^2-\\left(\\sqrt{4x^2+1}\\right)^2}{2x-1+\\sqrt{4x^2+1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"245\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0644 \u0627\u0644\u062c\u0630\u0631 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-17beafd120a7fc185e1499671fb4421a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\frac{\\left(2x-1\\right)^2-\\left(4x^2+1\\right)}{2x-1+\\sqrt{4x^2+1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"218\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0646 \u0646\u062d\u0644 \u0627\u0644\u0647\u0648\u064a\u0629 \u0627\u0644\u0628\u0627\u0631\u0632\u0629 \u0644\u0645\u0631\u0628\u0639 \u0627\u0644\u0641\u0631\u0642:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a34cb3941c92a785c11c50ecaa1e438_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\frac{4x^2+1-4x-\\left(4x^2+1\\right)}{2x-1+\\sqrt{4x^2+1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"245\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0646 \u0646\u0639\u0645\u0644 \u0641\u064a \u0627\u0644\u0628\u0633\u0637: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1a2e8d86f22087e775650d36bf78e719_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\frac{4x^2+1-4x-4x^2-1}{2x-1+\\sqrt{4x^2+1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"228\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2f25890bccb1eaa4c7aa7338f3a25f6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to +\\infty}\\frac{-4x}{2x-1+\\sqrt{4x^2+1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"195\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u062d\u0633\u0628 \u0642\u064a\u0645\u0629 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0639\u0646\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6986ded778a6220e3ad9d6c6bf873451_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to +\\infty} \\cfrac{-4x }{2x-1 +\\sqrt{4x^2+1} } = \\cfrac{-4(+\\infty) }{2(+\\infty)+\\sqrt{4(+\\infty)^2} } = \\cfrac{-\\infty}{+\\infty} =\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"458\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0648\u062c\u0648\u062f \u0645\u0631\u0628\u0639 x \u0641\u064a \u0627\u0644\u0645\u0642\u0627\u0645\u060c \u0625\u0644\u0627 \u0623\u0646 \u062f\u0631\u062c\u062a\u0647 \u0647\u064a \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639 1 \u0644\u0623\u0646\u0647 \u0645\u0648\u062c\u0648\u062f \u062f\u0627\u062e\u0644 \u0627\u0644\u062c\u0630\u0631:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0decc88d206f476d332becb025b8eeaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{4x^2} =\\sqrt{4}\\cdot \\sqrt{x^2} = \\sqrt{4}\\cdot x^{2\/2} =\\sqrt{4} x^1=\\sqrt{4}x .\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"351\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0646\u062a\u064a\u062c\u0629 \u0639\u062f\u0645 \u0627\u0644\u062a\u0639\u064a\u064a\u0646 -\u221e\/+\u221e \u0647\u064a \u062a\u0642\u0633\u064a\u0645 \u0645\u0639\u0627\u0645\u0644\u0627\u062a x \u0645\u0646 \u0627\u0644\u062f\u0631\u062c\u0629 \u0627\u0644\u0623\u0639\u0644\u0649\u060c \u0644\u0623\u0646 \u062f\u0631\u062c\u0629 \u0627\u0644\u0628\u0633\u0637 \u0647\u064a \u0646\u0641\u0633 \u062f\u0631\u062c\u0629 \u0627\u0644\u0645\u0642\u0627\u0645.<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8eb19af7ca51c14245db81bd6781b881_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\frac{-4x}{2x-1+\\sqrt{4x^2+1} }=\\frac{-\\infty}{+\\infty}=\\frac{-4}{2+\\sqrt{4}}=\\frac{-4}{2+2}=\\frac{-4}{4}=\\bm{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"499\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0627\u062d\u0638 \u0623\u0646\u0647 \u0646\u0638\u0631\u064b\u0627 \u0644\u0648\u062c\u0648\u062f \u062d\u062f\u064a\u0646 \u0645\u0646 \u0627\u0644\u062f\u0631\u062c\u0629 \u0627\u0644\u0623\u0648\u0644\u0649 \u0641\u064a \u0627\u0644\u0645\u0642\u0627\u0645<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c973910499b6b5a4828e213dc33f948d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl(2x\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -7px;\"><\/p>\n<p> \u0648<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c623cb17f27418239e3fcf7c2ec09946_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{4x^2}\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"46\" style=\"vertical-align: -7px;\"><\/p>\n<p> \u060c \u0644\u062d\u0644 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f -\u221e\/+\u221e \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u0623\u062e\u0630 \u062c\u0645\u064a\u0639 \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u062d\u062f\u0648\u062f \u0627\u0644\u062f\u0631\u062c\u0629 \u0627\u0644\u0623\u0648\u0644\u0649\u060c \u0623\u064a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0644<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-da4556c0a02b580047678d308649edf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0648 \u0627\u0644<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-65ddaa07508d3929b6969a5e4e6baddf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"23\" style=\"vertical-align: -2px;\"><\/p>\n<p> \u0644 <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4e8a851efdbfbb4531c82837d5a61edd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{4x^2}.\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"44\" style=\"vertical-align: -1px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u0627\u0644\u062a\u0645\u0631\u064a\u0646 7<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u062d\u0633\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 \u062a\u0642\u062a\u0631\u0628 x \u0645\u0646 1 \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0628\u0627\u0644\u0643\u0633\u0648\u0631: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-480bb119c1303a7afa394d812b0e7602_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 1}\\left(\\frac{1}{1-x}-\\frac{3}{1-x^3}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"173\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0645\u062d\u0627\u0648\u0644\u0629 \u0644\u062c\u0639\u0644 \u0627\u0644\u0646\u0647\u0627\u064a\u0629\u060c \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u063a\u064a\u0631 \u0627\u0644\u0645\u062d\u062f\u062f\u0629 \u0644\u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629 \u0646\u0627\u0642\u0635 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d11d45ea6681f3645773f6e0df8cce9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 1}\\left(\\frac{1}{1-x}-\\frac{3}{1-x^3}\\right)=\\frac{1}{1-1}--\\frac{3}{1-1^3}=\\frac{1}{0}-\\frac{3}{0}=\\bm{\\infty-\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"480\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0644\u0630\u0644\u0643 \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0627\u062e\u062a\u0632\u0627\u0644 \u0627\u0644\u0643\u0633\u0648\u0631 \u0625\u0644\u0649 \u0645\u0642\u0627\u0645 \u0645\u0634\u062a\u0631\u0643\u060c \u0623\u0648 \u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0636\u0631\u0628 \u0628\u0633\u0637 \u0648\u0645\u0642\u0627\u0645 \u0623\u062d\u062f \u0627\u0644\u0643\u0633\u0631\u064a\u0646 \u0641\u064a \u0645\u0642\u0627\u0645 \u0627\u0644\u0622\u062e\u0631:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-75bf3ffa177f32711c5509ce5fe5992d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x \\to 1}\\left(\\frac{1}{1-x}-\\frac{3}{1-x^3} \\right)=\\\\[5ex]\\displaystyle =\\lim_{x\\to 1}\\left( \\frac{1\\cdot(1-x^3)}{(1-x)\\cdot(1-x^3)}-\\frac{3\\cdot(1-x)}{(1-x^3)\\cdot(1-x)}\\right)=\\\\[5ex]\\displaystyle =\\lim_{x \\to 1}\\left(\\frac{1-x^3}{1-x-x^3+x^4}-\\frac{3-3x}{1-x-x^3+x^4}\\right)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"186\" width=\"382\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0645\u0627 \u0623\u0646 \u0627\u0644\u0643\u0633\u0631\u064a\u0646 \u0627\u0644\u0622\u0646 \u0644\u0647\u0645\u0627 \u0646\u0641\u0633 \u0627\u0644\u0645\u0642\u0627\u0645\u060c \u0641\u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u062c\u0645\u064a\u0639\u0647\u0645\u0627 \u0645\u0639\u064b\u0627:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c381a263e89e5a60ff0e6df9367a8ab1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1}\\left(\\frac{1-x^3}{1-x-x^3+x^4}-\\frac{3-3x}{1-x-x^3+x^4}\\right)=\\lim_{x\\to 1}\\frac{1-x^3-(3-3x)}{1-x-x^3+x^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"517\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0646 \u0646\u0639\u0645\u0644: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-05279cd25d55f5c50edfb5f82929701b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1} \\cfrac{1-x^3-3+3x}{1-x-x^3+x^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"153\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-818107141eb339d788408e23078ddda9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1} \\cfrac{-x^3+3x-2}{x^4-x^3-x+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"153\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0646\u062d\u0627\u0648\u0644 \u062d\u0644 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0645\u0631\u0629 \u0623\u062e\u0631\u0649:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9d0a31b51faff7e77e778fba66fdbaa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1}\\frac{-x^3+3x-2}{x^4-x^3-x+1}=\\frac{-1^3+3\\cdot1-2}{1^4-1^3-1+1}=\\mathbf{\\frac{0}{0}}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"335\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0643\u0646\u0646\u0627 \u0646\u062c\u062f \u0639\u062f\u0645 \u0627\u0644\u062a\u0639\u064a\u064a\u0646 \u0635\u0641\u0631\u064b\u0627 \u0645\u0642\u0633\u0648\u0645\u064b\u0627 \u0639\u0644\u0649 \u0635\u0641\u0631. \u0644\u0630\u0644\u0643 \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u062a\u062d\u0644\u064a\u0644 \u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f \u0641\u064a \u0627\u0644\u0628\u0633\u0637 \u0648\u0627\u0644\u0645\u0642\u0627\u0645:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e5b8321a511b5e370abe8844bf9624ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1}\\frac{-x^3+3x-2}{x^4-x^3-x+1}=\\lim_{x \\to 1}\\frac{-(x-1)^2(x+2)}{(x-1)^2(x^2+x+1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"369\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0642\u0648\u0645 \u0627\u0644\u0622\u0646 \u0628\u062a\u0628\u0633\u064a\u0637 \u0627\u0644\u0643\u0633\u0631 \u0628\u0625\u0632\u0627\u0644\u0629 \u0627\u0644\u0639\u0627\u0645\u0644 \u0627\u0644\u0630\u064a \u064a\u062a\u0643\u0631\u0631 \u0641\u064a \u0627\u0644\u0628\u0633\u0637 \u0648\u0627\u0644\u0645\u0642\u0627\u0645:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ab5629bd2fabeb755da37d3abea335b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1}\\frac{-\\cancel{(x-1)^2}(x+2)}{\\cancel{(x-1)^2}(x^2+x+1)}=\\lim_{x \\to 1}\\frac{-(x+2)}{x^2+x+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"329\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u062d\u0644 \u0627\u0644\u062d\u062f: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dbb1676133fe1e33fb4d18078b945959_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1}\\frac{-(x+2)}{x^2+x+1}=\\frac{-(1+2)}{1^2+1+1}=\\frac{-3}{3}=\\bm{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"316\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0646\u0634\u0631\u062d \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629 \u0643\u064a\u0641\u064a\u0629 \u062d\u0644 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0646\u0627\u0642\u0635 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a (\u221e-\u221e). \u0633\u062a\u062c\u062f \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0647\u0630\u0627 \u0645\u0639 \u0623\u0646\u0648\u0627\u0639 \u0645\u062e\u062a\u0644\u0641\u0629 \u0645\u0646 \u0627\u0644\u0648\u0638\u0627\u0626\u0641\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0645\u0646 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0646\u0627\u0642\u0635 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a. \u062d\u0644 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0646\u0627\u0642\u0635 \u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0639\u0646\u062f\u0645\u0627 \u062a\u0639\u0637\u064a \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d8%b9%d8%af%d9%85-%d8%a7%d9%84%d8%aa%d8%ad%d8%af%d9%8a%d8%af-%d9%84%d8%a7-%d9%86%d9%87%d8%a7%d8%a6%d9%8a-%d9%86%d8%a7%d9%82%d8%b5-%d9%84%d8%a7-%d9%86%d9%87%d8%a7%d8%a6%d9%8a-%e2%88%9e-%e2%88%9e\/\"> <span class=\"screen-reader-text\">\u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u062f\u064a\u062f \u0644\u0627\u0646\u0647\u0627\u0626\u064a \u0646\u0627\u0642\u0635 \u0644\u0627\u0646\u0647\u0627\u0626\u064a (\u221e-\u221e)<\/span> \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[11],"tags":[],"class_list":["post-378","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized 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