{"id":20,"date":"2023-09-17T11:09:22","date_gmt":"2023-09-17T11:09:22","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d8%ae%d8%b5%d8%a7%d8%a6%d8%b5-%d9%82%d9%88%d8%a7%d9%86%d9%8a%d9%86-%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af\/"},"modified":"2023-09-17T11:09:22","modified_gmt":"2023-09-17T11:09:22","slug":"%d8%ae%d8%b5%d8%a7%d8%a6%d8%b5-%d9%82%d9%88%d8%a7%d9%86%d9%8a%d9%86-%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d8%ae%d8%b5%d8%a7%d8%a6%d8%b5-%d9%82%d9%88%d8%a7%d9%86%d9%8a%d9%86-%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af\/","title":{"rendered":"\u062e\u0635\u0627\u0626\u0635 (\u0623\u0648 \u0642\u0648\u0627\u0646\u064a\u0646) \u0627\u0644\u062d\u062f\u0648\u062f"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0633\u062a\u062c\u062f \u0647\u0646\u0627 \u062c\u0645\u064a\u0639 \u062e\u0635\u0627\u0626\u0635 (\u0623\u0648 \u0642\u0648\u0627\u0646\u064a\u0646) \u062d\u062f\u0648\u062f \u0627\u0644\u0648\u0638\u0627\u0626\u0641. \u062a\u0639\u0645\u0644 \u0647\u0630\u0647 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0639\u0644\u0649 \u062a\u0628\u0633\u064a\u0637 \u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a\u060c \u062e\u0627\u0635\u0629 \u0639\u0646\u062f \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0645\u0639 \u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u062f\u0627\u0644\u0629. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"%c2%bfcuales-son-las-propiedades-o-leyes-de-los-limites-de-funciones\"><\/span> \u0645\u0627 \u0647\u064a \u062e\u0635\u0627\u0626\u0635 (\u0623\u0648 \u0642\u0648\u0627\u0646\u064a\u0646) \u062d\u062f\u0648\u062f \u0627\u0644\u0648\u0638\u0627\u0626\u0641\u061f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0639\u062f \u0630\u0644\u0643\u060c \u0633\u0646\u0634\u0631\u062d \u062c\u0645\u064a\u0639 \u062e\u0635\u0627\u0626\u0635 \u062d\u062f\u0648\u062f \u0627\u0644\u062f\u0648\u0627\u0644\u060c \u0623\u0648 \u0645\u0627 \u064a\u0633\u0645\u0649 \u0623\u064a\u0636\u064b\u0627 \u0628\u0642\u0648\u0627\u0646\u064a\u0646 \u062d\u062f\u0648\u062f \u0627\u0644\u062f\u0648\u0627\u0644. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0631\u0624\u064a\u0629 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0645\u062d\u0644\u0648\u0644\u0629 \u0644\u0643\u0644 \u062e\u0627\u0635\u064a\u0629 \u0645\u0646 \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u062d\u062a\u0649 \u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0641\u0647\u0645 \u0627\u0644\u0645\u0641\u0647\u0648\u0645 \u0628\u0634\u0643\u0644 \u0643\u0627\u0645\u0644.<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"propiedad-del-limite-de-una-suma\"><\/span> \u062e\u0627\u0635\u064a\u0629 \u062d\u062f \u0627\u0644\u0645\u0628\u0644\u063a <span class=\"ez-toc-section-end\"><\/span><\/h3>\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\"> <strong>\u0646\u0647\u0627\u064a\u0629 \u0645\u062c\u0645\u0648\u0639 \u062f\u0627\u0644\u062a\u064a\u0646<\/strong> \u0639\u0646\u062f \u0646\u0642\u0637\u0629 \u0645\u0627 \u062a\u0633\u0627\u0648\u064a \u0645\u062c\u0645\u0648\u0639 \u062d\u062f\u0648\u062f \u0643\u0644 \u062f\u0627\u0644\u0629 \u0639\u0646\u062f \u0646\u0641\u0633 \u0627\u0644\u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u062d\u062f\u0629.<\/p>\n<\/div>\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-e1975fcd0e98e2022e29be694fcdb925_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to a} \\Bigl[ f(x)+g(x)\\Bigr]=\\lim_{x\\to a}f(x)+\\lim_{x\\to a}g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"310\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0644\u0646\u0641\u062a\u0631\u0636 \u0623\u0646 \u0647\u0646\u0627\u0643 \u0648\u0638\u064a\u0641\u062a\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-1730973da231e978e4c565c939633b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2\\qquad g(x)=2x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"217\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u0647\u0627\u064a\u0629 \u0643\u0644 \u062f\u0627\u0644\u0629 \u0639\u0646\u062f x \u062a\u0633\u0627\u0648\u064a 1 \u0647\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-540347d33b8f0dc2d46cbc8d6f42df12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to 1}x^2=1^2=1\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"121\" style=\"vertical-align: -12px;\"><\/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-9e8d60234a5aaad645bcea92331ffec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to 1}(2x+1)=2\\cdot1+1=3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"209\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u062a\u064a\u0646 \u0627\u0644\u0645\u0636\u0627\u0641\u062a\u064a\u0646 \u0639\u0646\u062f \u0646\u0641\u0633 \u0627\u0644\u0646\u0642\u0637\u0629 \u062a\u0639\u0637\u064a 4 (1+3=4).<\/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-dee2fbc7ec3a4f0a145e79c1f8bf9ae2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x\\to 1} \\Bigl[ f(x)+g(x)\\Bigr]=\\\\[3ex]\\displaystyle =\\lim_{x\\to 1}f(x)+\\lim_{x\\to 1}g(x)=\\\\[3ex]=1+3=4\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"189\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u064a\u0645\u0643\u0646 \u0625\u062b\u0628\u0627\u062a \u0627\u0644\u062e\u0627\u0635\u064a\u0629 \u0639\u0646 \u0637\u0631\u064a\u0642 \u062d\u0633\u0627\u0628 \u0627\u0644\u062d\u062f \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-14c858a555a3d57a24cc5c81adeda2fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x\\to 1} \\Bigl[ f(x)+g(x)\\Bigr]=\\\\[3ex]\\displaystyle =\\lim_{x\\to 1}\\Bigl[x^2+2x+1\\Bigr]=\\\\[3ex]=1^2+2\\cdot 1+1=4\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"117\" width=\"171\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"propiedad-del-limite-de-una-resta\"><\/span> \u062e\u0627\u0635\u064a\u0629 \u062d\u062f \u0627\u0644\u0637\u0631\u062d <span class=\"ez-toc-section-end\"><\/span><\/h3>\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\"> <strong>\u0625\u0646 \u062d\u062f \u0627\u0644\u0637\u0631\u062d (\u0623\u0648 \u0627\u0644\u0641\u0631\u0642) \u0644\u0648\u0638\u064a\u0641\u062a\u064a\u0646<\/strong> \u0639\u0646\u062f \u0646\u0642\u0637\u0629 \u0645\u0627 \u064a\u0639\u0627\u062f\u0644 \u0637\u0631\u062d \u0646\u0647\u0627\u064a\u0629 \u0643\u0644 \u062f\u0627\u0644\u0629 \u0639\u0646\u062f \u0646\u0641\u0633 \u0627\u0644\u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u062d\u062f\u0629.<\/p>\n<\/div>\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-444c20b463064780542e57269cfd770e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to a} \\Bigl[ f(x)-g(x)\\Bigr]=\\lim_{x\\to a}f(x)-\\lim_{x\\to a}g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"310\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0648\u0638\u0627\u0626\u0641 \u0645\u0646 \u0627\u0644\u0645\u062b\u0627\u0644 \u0627\u0644\u0633\u0627\u0628\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-1730973da231e978e4c565c939633b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2\\qquad g(x)=2x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"217\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0647\u0627\u064a\u0629 \u0643\u0644 \u062f\u0627\u0644\u0629 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 x=3 \u0647\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-f37267a3dc92ccef5a66ccfb68211919_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to 3}x^2=3^2=9\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"122\" style=\"vertical-align: -12px;\"><\/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-64b82eccca7888756f96190e6374281a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to 3}(2x+1)=2\\cdot3+1=7\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"209\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0646\u060c \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u062a\u064a\u0646 \u0627\u0644\u0645\u0637\u0631\u0648\u062d\u062a\u064a\u0646 \u0639\u0646\u062f x=3 \u0647\u064a \u0641\u0631\u0642 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u062a\u064a \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0641\u064a \u0627\u0644\u062e\u0637\u0648\u0629 \u0627\u0644\u0633\u0627\u0628\u0642\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-85e829be6e72a7ab7bd91d442c89558f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x\\to 3} \\Bigl[ f(x)-g(x)\\Bigr]=\\\\[3ex]\\displaystyle =\\lim_{x\\to 3}f(x)-\\lim_{x\\to 3}g(x)=\\\\[3ex]=9-7=2\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"110\" width=\"189\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646\u0646\u0627 \u0625\u062b\u0628\u0627\u062a \u062e\u0627\u0635\u064a\u0629 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0647\u0630\u0647 \u0639\u0646 \u0637\u0631\u064a\u0642 \u062d\u0633\u0627\u0628 \u0637\u0631\u062d \u0627\u0644\u062f\u0648\u0627\u0644 \u0648\u0645\u0646 \u062b\u0645 \u0625\u064a\u062c\u0627\u062f \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-411bbd6ad4e5d44322ec93ba06fd3088_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x\\to 3} \\Bigl[ f(x)-g(x)\\Bigr]=\\\\[3ex]\\displaystyle =\\lim_{x\\to 3}\\Bigl[x^2-(2x+1)\\Bigr]=\\\\[3ex]\\displaystyle =\\lim_{x\\to 3}\\Bigl[x^2-2x-1\\Bigr]\\\\[3ex]=3^2-2\\cdot 3-1=2\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"165\" width=\"185\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"propiedad-de-limite-de-un-producto\"><\/span> \u0627\u0644\u062d\u062f \u0645\u0646 \u0645\u0644\u0643\u064a\u0629 \u0627\u0644\u0645\u0646\u062a\u062c <span class=\"ez-toc-section-end\"><\/span><\/h3>\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\"> <strong>\u0646\u0647\u0627\u064a\u0629 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u062f\u0627\u0644\u062a\u064a\u0646<\/strong> \u0639\u0646\u062f \u0646\u0642\u0637\u0629 \u0645\u0627 \u0647\u064a \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0646\u0647\u0627\u064a\u0629 \u0643\u0644 \u062f\u0627\u0644\u0629 \u0639\u0646\u062f \u062a\u0644\u0643 \u0627\u0644\u0646\u0642\u0637\u0629.<\/p>\n<\/div>\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-d513f66b066a53d8dbd18868f1edcaa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to a} \\Bigl[ f(x)\\cdot g(x)\\Bigr]=\\lim_{x\\to a}f(x)\\cdot \\lim_{x\\to a}g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"292\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0625\u0630\u0627 \u0643\u0627\u0646 \u0644\u062f\u064a\u0646\u0627 \u0627\u0644\u0648\u0638\u064a\u0641\u062a\u064a\u0646 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u062a\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u062a\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-9c48ccc2acf27d4fb1519d80b4c0cbe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3\\qquad g(x)=x^2-5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"216\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0647\u0627\u064a\u0629 \u0643\u0644 \u062f\u0627\u0644\u0629 \u0639\u0646\u062f x=2 \u0647\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-eb87f9cfecaec2126043e52053704c82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to 2}x^3=2^3=8\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"122\" style=\"vertical-align: -12px;\"><\/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-c62f8966fd75151d6bdc8955458d1557_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to 2}(x^2-5)=2^2-5=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"207\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0644\u062a\u062d\u062f\u064a\u062f \u0646\u0647\u0627\u064a\u0629 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0627\u0644\u062f\u0627\u0644\u062a\u064a\u0646\u060c \u0644\u064a\u0633 \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u0636\u0631\u0628\u0647\u0645\u0627 \u0645\u0639\u064b\u0627\u060c \u0648\u0644\u0643\u0646 \u064a\u0643\u0641\u064a \u0636\u0631\u0628 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u062a\u064a \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0645\u0646 \u0643\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-0df37e873bf968f39617b8dce74edb9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x\\to 2} \\Bigl[ f(x)\\cdot g(x)\\Bigr]=\\\\[3ex]\\displaystyle =\\lim_{x\\to 2}f(x)\\cdot \\lim_{x\\to 2}g(x)=\\\\[3ex]=8\\cdot (-1)=-8\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"115\" width=\"180\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0647\u0630\u0627 \u064a\u0648\u0641\u0631 \u0639\u0644\u064a\u0646\u0627 \u0627\u0644\u0648\u0642\u062a \u0648\u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0644\u0623\u0646 \u0636\u0631\u0628 \u0648\u0638\u064a\u0641\u062a\u064a\u0646 \u0642\u062f \u064a\u0643\u0648\u0646 \u0623\u0645\u0631\u064b\u0627 \u0635\u0639\u0628\u064b\u0627. <\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"propiedad-del-limite-de-un-cociente\"><\/span> \u062e\u0627\u0635\u064a\u0629 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062d\u0627\u0635\u0644 <span class=\"ez-toc-section-end\"><\/span><\/h3>\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\"> <strong>\u062d\u062f \u062d\u0627\u0635\u0644 (\u0623\u0648 \u0627\u0644\u0642\u0633\u0645\u0629) \u0644\u0648\u0638\u064a\u0641\u062a\u064a\u0646<\/strong> \u064a\u0633\u0627\u0648\u064a \u062d\u0627\u0635\u0644 \u062d\u062f\u0648\u062f \u0627\u0644\u062f\u0627\u0644\u062a\u064a\u0646.<\/p>\n<\/div>\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-dbb038d24d534af7fc12466761b1206c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to a} \\left[\\frac{f(x)}{g(x)}\\right]=\\frac{\\displaystyle\\lim_{x\\to a}f(x)}{\\displaystyle\\lim_{x\\to a}g(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"181\" style=\"vertical-align: -24px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u062a\u062d\u0642\u0642 \u0647\u0630\u0627 \u0627\u0644\u0634\u0631\u0637 \u0637\u0627\u0644\u0645\u0627 \u0623\u0646 \u0646\u0647\u0627\u064a\u0629 \u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u0642\u0627\u0645 \u0644\u064a\u0633\u062a \u0635\u0641\u0631\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-615afb4e193ec9b817d1672cb66f67b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to a}g(x)\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"97\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0633\u0648\u0641 \u0646\u0642\u0648\u0645 \u0628\u062d\u0644 \u0645\u062b\u0627\u0644 \u0644\u0647\u0630\u0647 \u0627\u0644\u062e\u0627\u0635\u064a\u0629 (\u0623\u0648 \u0627\u0644\u0642\u0627\u0646\u0648\u0646) \u0644\u0644\u062d\u062f\u0648\u062f. \u062e\u0630 \u0628\u0639\u064a\u0646 \u0627\u0644\u0627\u0639\u062a\u0628\u0627\u0631 \u0627\u0644\u062f\u0627\u0644\u062a\u064a\u0646 f(x) \u0648g(x):<\/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-193a456033487c8b6501aa861a1b6351_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=5x-1\\qquad g(x)=3^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"217\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0633\u0628 \u0623\u0648\u0644\u0627\u064b \u0646\u0647\u0627\u064a\u0629 \u0643\u0644 \u062f\u0627\u0644\u0629 \u0639\u0646\u062f x=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-a25aaef5c60bc849e2cfe326093a82fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to 0}(5x-1)=5\\cdot 0-1=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"222\" style=\"vertical-align: -12px;\"><\/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-40be0b69270ff2804525ec6aa35a934c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to 0}3^x=3^0=1\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"121\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u064a\u0645\u0643\u0646 \u0627\u0644\u0639\u062b\u0648\u0631 \u0628\u0633\u0647\u0648\u0644\u0629 \u0639\u0644\u0649 \u062d\u062f \u062a\u0642\u0633\u064a\u0645 \u0627\u0644\u062f\u0627\u0644\u062a\u064a\u0646 \u0639\u0646\u062f x=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-e8558b623352036e3af2e68e72861b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x\\to 0} \\left[\\frac{f(x)}{g(x)}\\right]=\\frac{\\displaystyle\\lim_{x\\to 0}f(x)}{\\displaystyle\\lim_{x\\to 0}g(x)}=\\displaystyle\\frac{-1}{1}=-1\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"278\" style=\"vertical-align: -24px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u0637\u0628\u064a\u0642 \u0647\u0630\u0647 \u0627\u0644\u062e\u0627\u0635\u064a\u0629 \u0644\u062d\u0644 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0644\u0623\u0646 \u0646\u0647\u0627\u064a\u0629 g(x) \u0644\u064a\u0633\u062a \u0635\u0641\u0631\u064b\u0627. <\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"propiedad-del-limite-de-una-constante\"><\/span> \u062e\u0627\u0635\u064a\u0629 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062b\u0627\u0628\u062a <span class=\"ez-toc-section-end\"><\/span><\/h3>\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\"> <strong>\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062b\u0627\u0628\u062a\u0629<\/strong> \u062a\u0624\u062f\u064a \u062f\u0627\u0626\u0645\u064b\u0627 \u0625\u0644\u0649 \u0627\u0644\u062b\u0627\u0628\u062a \u0646\u0641\u0633\u0647\u060c \u0628\u063a\u0636 \u0627\u0644\u0646\u0638\u0631 \u0639\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u0639\u0646\u062f\u0647\u0627 \u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629.<\/p>\n<\/div>\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-083ac97d4077fd32108f371887a6daef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to a} k=k\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"74\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0627\u0644\u0633\u0647\u0644 \u062c\u062f\u064b\u0627 \u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u062e\u0627\u0635\u064a\u0629\u060c \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0644\u062f\u064a\u0646\u0627 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062b\u0627\u0628\u062a\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-e9e41bd168999d7634188ca08496465a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646\u0637\u0642\u064a\u064b\u0627\u060c \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062b\u0627\u0628\u062a\u0629 \u0639\u0646\u062f \u0623\u064a \u0646\u0642\u0637\u0629 \u0647\u064a 5: <\/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-cc495627062fe120c4fba7c649b94ea8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to 0}5=5\\qquad\\qquad\\lim_{x\\to 3}5=5\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"218\" style=\"vertical-align: -12px;\"><\/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-bf06e3dadceb69c684be4e04205744f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to -2}5=5\\qquad\\qquad\\lim_{x\\to 7}5=5\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"229\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"propiedad-del-limite-de-un-multiplo-constante\"><\/span> \u062e\u0627\u0635\u064a\u0629 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0645\u0636\u0627\u0639\u0641 \u0627\u0644\u062b\u0627\u0628\u062a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0646 \u062e\u0648\u0627\u0635 \u0646\u0647\u0627\u064a\u0629 \u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0648\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062b\u0627\u0628\u062a \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0627\u0644\u062e\u0627\u0635\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629: <\/p>\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\"> <strong>\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u0636\u0631\u0648\u0628\u0629 \u0641\u064a \u062b\u0627\u0628\u062a<\/strong> \u062a\u0633\u0627\u0648\u064a \u0646\u0627\u062a\u062c \u0627\u0644\u062b\u0627\u0628\u062a \u0627\u0644\u0645\u0630\u0643\u0648\u0631 \u0648\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629.<\/p>\n<\/div>\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-9e11e20d92c504cfb48a1a5c3747066f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to a}\\Bigl[ k\\cdot f(x)\\Bigr]=k\\cdot\\lim_{x\\to a}f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"214\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0627\u062d\u0638 \u0643\u064a\u0641 \u0642\u0645\u0646\u0627 \u0628\u062a\u0628\u0633\u064a\u0637 \u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0647 \u0627\u0644\u062e\u0627\u0635\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-422e706a1b7643d78c0d667e17ede188_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle \\lim_{x\\to 4} (2x^2-12x+10)=\\\\[3ex]\\displaystyle =\\lim_{x\\to 4}\\Bigl[2\\cdot(x^2-6x+5)\\Bigr]=\\\\[3ex]=\\displaystyle 2\\cdot\\lim_{x\\to 4}(x^2-6x+5)=\\\\[3ex]=2\\cdot (4^2-6\\cdot4+5)=\\\\[3ex]=2\\cdot (-3)=-6\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"206\" width=\"206\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"propiedad-del-limite-de-una-potencia\"><\/span> \u062e\u0627\u0635\u064a\u0629 \u062d\u062f \u0627\u0644\u0642\u0648\u0629 <span class=\"ez-toc-section-end\"><\/span><\/h3>\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\"> <strong>\u0646\u0647\u0627\u064a\u0629 \u0623\u064a \u062f\u0627\u0644\u0629 \u0645\u0631\u0641\u0648\u0639\u0629 \u0625\u0644\u0649 \u0627\u0644\u0623\u0633<\/strong> \u062a\u0639\u0627\u062f\u0644 \u062d\u0633\u0627\u0628 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u062b\u0645 \u0631\u0641\u0639 \u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643 \u0627\u0644\u0623\u0633.<\/p>\n<\/div>\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-02b8185a9eca6e85f4d3e69b41b09903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to a}\\Bigl[f(x)^k\\Bigr]=\\left[\\lim_{x\\to a}f(x)\\right]^k\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"202\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062e\u0637\u064a\u0629 \u0647\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-73523d73bd77b077f64d5bf05bd0444c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 6}x=6\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"74\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u0633\u0646\u064b\u0627\u060c \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a\u0629 \u0628\u0625\u064a\u062c\u0627\u062f \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062e\u0637\u064a\u0629 \u062b\u0645 \u062a\u0631\u0628\u064a\u0639 \u0627\u0644\u0646\u062a\u064a\u062c\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-051ef387f34fdcc7468d761e2d618f69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 6}\\Bigl[x^2\\Bigr]=\\left[\\lim_{x\\to 6}x\\right]^2=\\bigl[6\\bigr]^2=36\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"249\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"propiedad-del-limite-de-una-funcion-exponencial\"><\/span> \u062e\u0627\u0635\u064a\u0629 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 <span class=\"ez-toc-section-end\"><\/span><\/h3>\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\"> <strong>\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629<\/strong> \u062a\u0633\u0627\u0648\u064a \u062b\u0627\u0628\u062a \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u0631\u0641\u0648\u0639\u064b\u0627 \u0625\u0644\u0649 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062c\u0628\u0631\u064a \u0644\u0644\u062f\u0627\u0644\u0629.<\/p>\n<\/div>\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-a2fc0c424758574c4b22a93c3e5dfdcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to a}\\Bigl[k^{g(x)}\\Bigr]=k^{^{\\displaystyle\\lim_{x\\to a}g(x)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"179\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0633\u0646\u0642\u0648\u0645 \u0628\u0639\u062f \u0630\u0644\u0643 \u0628\u062d\u0633\u0627\u0628 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629 \u0628\u0637\u0631\u064a\u0642\u062a\u064a\u0646 \u0645\u0645\u0643\u0646\u062a\u064a\u0646 \u0644\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u062e\u0627\u0635\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-6eb8d552dbdff46188019ca7d717e5a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 1}5^{2x}=5^{2\\cdot 1}=25\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"147\" style=\"vertical-align: -12px;\"><\/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-1088a10d675c2a6dc332c23a362fce2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 1}5^{2x}=5^{^{\\displaystyle\\lim_{x\\to 1}2x}}=5^{2\\cdot 1}=25\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"232\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"propiedad-del-limite-de-una-potencia-de-funciones\"><\/span> \u062e\u0627\u0635\u064a\u0629 \u0627\u0644\u062d\u062f \u0645\u0646 \u0642\u0648\u0629 \u0627\u0644\u0648\u0638\u0627\u0626\u0641 <span class=\"ez-toc-section-end\"><\/span><\/h3>\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\"> <strong>\u0646\u0647\u0627\u064a\u0629 \u062f\u0627\u0644\u0629 \u0645\u0631\u0641\u0648\u0639\u0629 \u0625\u0644\u0649 \u062f\u0627\u0644\u0629 \u0623\u062e\u0631\u0649<\/strong> \u0647\u064a \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0648\u0644\u0649 \u0645\u0631\u0641\u0648\u0639\u0629 \u0625\u0644\u0649 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062b\u0627\u0646\u064a\u0629.<\/p>\n<\/div>\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-11395cf067e1c7ff75ae68090bec8d16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x\\to a}\\Bigl[f(x)^{g(x)}\\Bigr]=\\left[\\lim_{x\\to a}f(x)\\right]^{\\displaystyle\\lim_{x\\to a}g(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"277\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644 \u0633\u0646\u062d\u062f\u062f \u0627\u0644\u062d\u062f \u0627\u0644\u062a\u0627\u0644\u064a \u0628\u062a\u0637\u0628\u064a\u0642 \u0647\u0630\u0627 \u0627\u0644\u0642\u0627\u0646\u0648\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-88cf4a1a6c04abab530e67f4f0ca950d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x\\to 2}\\Bigl[(x^2-4x)^{4x-5}\\Bigr]=\\\\[3ex]\\displaystyle =\\left[\\lim_{x\\to 2}(x^2-4x)\\right]^{\\displaystyle\\lim_{x\\to 2}(4x-5)}=\\\\[3ex]=\\displaystyle (2^2-4\\cdot 2)^{4\\cdot 2-5}=\\\\[3ex]=(-4)^3=-64\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"173\" width=\"247\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"propiedad-del-limite-de-una-funcion-irracional\"><\/span> \u062e\u0627\u0635\u064a\u0629 \u0646\u0647\u0627\u064a\u0629 \u062f\u0627\u0644\u0629 \u063a\u064a\u0631 \u0639\u0642\u0644\u0627\u0646\u064a\u0629 <span class=\"ez-toc-section-end\"><\/span><\/h3>\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\"> <strong>\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062c\u0630\u0631 (\u0623\u0648 \u0627\u0644\u062c\u0630\u0631)<\/strong> \u062a\u0633\u0627\u0648\u064a \u062c\u0630\u0631 \u0627\u0644\u0646\u0647\u0627\u064a\u0629.<\/p>\n<\/div>\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-2cdf7e1a72f2441f72240f068edc413e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to a}\\sqrt[n]{f(x)}=\\sqrt[n]{\\lim_{x\\to a}f(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"197\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0647 \u0627\u0644\u062e\u0627\u0635\u064a\u0629\u060c \u064a\u062c\u0628 \u0623\u0646 \u062a\u0636\u0639 \u0641\u064a \u0627\u0639\u062a\u0628\u0627\u0631\u0643 \u0623\u0646\u0647 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0641\u0647\u0631\u0633 \u0627\u0644\u062c\u0630\u0631 \u0632\u0648\u062c\u064a\u064b\u0627\u060c \u0641\u064a\u062c\u0628 \u0623\u0646 \u064a\u0643\u0648\u0646 \u062d\u062f \u0627\u0644\u062f\u0627\u0644\u0629 \u0623\u0643\u0628\u0631 \u0645\u0646 \u0623\u0648 \u064a\u0633\u0627\u0648\u064a 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-31077c9693c2318fba7cb2f0f99d5efd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{si } n \\text{ es par} \\ \\longrightarrow \\ \\displaystyle\\lim_{x\\to a}f(x)\\ge 0\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"230\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0627\u062d\u0638 \u0643\u064a\u0641 \u062a\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0628\u062a\u0637\u0628\u064a\u0642 \u0647\u0630\u0647 \u0627\u0644\u0635\u064a\u063a\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-ad822bfcdd6fbb0335e1d99db71776c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 4}\\sqrt[3]{\\frac{x^2}{2}}=\\sqrt[3]{\\lim_{x\\to 4}\\frac{x^2}{2}}=\\sqrt[3]{\\frac{4^2}{2}}=\\sqrt[3]{8}=2\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"310\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"propiedad-del-limite-de-una-funcion-logaritmica\"><\/span> \u062e\u0627\u0635\u064a\u0629 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u064a\u0629 <span class=\"ez-toc-section-end\"><\/span><\/h3>\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\"> <strong>\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645<\/strong> \u062a\u0639\u0627\u062f\u0644 \u0646\u0641\u0633 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645 \u0627\u0644\u0623\u0633\u0627\u0633\u064a \u0644\u0644\u062d\u062f.<\/p>\n<\/div>\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-6e34ee6ca0162d42714f0c8f3e245b14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to a}\\Bigl[\\log_k f(x)\\Bigr]=\\log_k \\left[\\lim_{x\\to a}f(x)\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"252\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0646\u0638\u0631 \u0625\u0644\u0649 \u062d\u0644 \u0627\u0644\u062d\u062f \u0627\u0644\u062a\u0627\u0644\u064a \u0627\u0644\u0630\u064a \u0646\u0637\u0628\u0642 \u0641\u064a\u0647 \u0647\u0630\u0647 \u0627\u0644\u062e\u0627\u0635\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-fc5468c73e74d00d2ffeb2293ea8145e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x\\to -4}\\Bigl[\\log_3 (x^2-2x+3)\\Bigr]=\\\\[3ex]=\\displaystyle\\log_3 \\left[\\lim_{x\\to -4}(x^2-2x+3)\\right]=\\\\[4ex]=\\displaystyle\\log_3\\bigl[(-4)^2-2\\cdot (-4)+3\\bigr]=\\\\[3ex]=\\displaystyle\\log_3 27=3\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"177\" width=\"236\" style=\"vertical-align: 0px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0633\u062a\u062c\u062f \u0647\u0646\u0627 \u062c\u0645\u064a\u0639 \u062e\u0635\u0627\u0626\u0635 (\u0623\u0648 \u0642\u0648\u0627\u0646\u064a\u0646) \u062d\u062f\u0648\u062f \u0627\u0644\u0648\u0638\u0627\u0626\u0641. \u062a\u0639\u0645\u0644 \u0647\u0630\u0647 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0639\u0644\u0649 \u062a\u0628\u0633\u064a\u0637 \u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a\u060c \u062e\u0627\u0635\u0629 \u0639\u0646\u062f \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0645\u0639 \u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u062f\u0627\u0644\u0629. \u0645\u0627 \u0647\u064a \u062e\u0635\u0627\u0626\u0635 (\u0623\u0648 \u0642\u0648\u0627\u0646\u064a\u0646) \u062d\u062f\u0648\u062f \u0627\u0644\u0648\u0638\u0627\u0626\u0641\u061f \u0628\u0639\u062f \u0630\u0644\u0643\u060c \u0633\u0646\u0634\u0631\u062d \u062c\u0645\u064a\u0639 \u062e\u0635\u0627\u0626\u0635 \u062d\u062f\u0648\u062f \u0627\u0644\u062f\u0648\u0627\u0644\u060c \u0623\u0648 \u0645\u0627 \u064a\u0633\u0645\u0649 \u0623\u064a\u0636\u064b\u0627 \u0628\u0642\u0648\u0627\u0646\u064a\u0646 \u062d\u062f\u0648\u062f \u0627\u0644\u062f\u0648\u0627\u0644. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0631\u0624\u064a\u0629 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0645\u062d\u0644\u0648\u0644\u0629 \u0644\u0643\u0644 \u062e\u0627\u0635\u064a\u0629 \u0645\u0646 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" 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