{"id":378,"date":"2023-07-04T04:08:40","date_gmt":"2023-07-04T04:08:40","guid":{"rendered":"https:\/\/mathority.org\/ko\/%eb%b6%88%ed%99%95%ec%a0%95-%eb%ac%b4%ed%95%9c-%eb%a7%88%ec%9d%b4%eb%84%88%ec%8a%a4-%eb%ac%b4%ed%95%9c-%e2%88%9e-%e2%88%9e\/"},"modified":"2023-07-04T04:08:40","modified_gmt":"2023-07-04T04:08:40","slug":"%eb%b6%88%ed%99%95%ec%a0%95-%eb%ac%b4%ed%95%9c-%eb%a7%88%ec%9d%b4%eb%84%88%ec%8a%a4-%eb%ac%b4%ed%95%9c-%e2%88%9e-%e2%88%9e","status":"publish","type":"post","link":"https:\/\/mathority.org\/ko\/%eb%b6%88%ed%99%95%ec%a0%95-%eb%ac%b4%ed%95%9c-%eb%a7%88%ec%9d%b4%eb%84%88%ec%8a%a4-%eb%ac%b4%ed%95%9c-%e2%88%9e-%e2%88%9e\/","title":{"rendered":"\ubd88\ud655\uc815\uc131 \ubb34\ud55c \ub9c8\uc774\ub108\uc2a4 \ubb34\ud55c(\ubb34\ud55c\ub300-\ubb34\ud55c\ub300)"},"content":{"rendered":"<p>\uc774 \uae30\uc0ac\uc5d0\uc11c\ub294 \ubb34\ud55c \ube7c\uae30 \ubb34\ud55c(\ubb34\ud55c\ub300-\ubb34\ud55c\ub300) \ubd88\ud655\uc815\uc131\uc744 \ud574\uacb0\ud558\ub294 \ubc29\ubc95\uc744 \uc124\uba85\ud569\ub2c8\ub2e4. \ub2e4\uc591\ud55c \uc720\ud615\uc758 \ud568\uc218\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc774\ub7ec\ud55c \ubd88\ud655\uc815\uc131\uc758 \uc608\ub97c \ucc3e\uc744 \uc218 \uc788\uc73c\uba70, \ucd94\uac00\ub85c \ubd88\ud655\uc815\uc131 \ubb34\ud55c &#8211; \ubb34\ud55c\uc758 \ub2e8\uacc4\ubcc4 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \uc5f0\uc2b5\uc744 \ud1b5\ud574 \uc5f0\uc2b5\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"resolver-la-indeterminacion-infinito-menos-infinito\"><\/span> \ubd88\ud655\uc815\uc131 \ubb34\ud55c \ub9c8\uc774\ub108\uc2a4 \ubb34\ud55c \ud480\uae30<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \ud568\uc218\uc758 \uadf9\ud55c\uc774 \ubb34\ud55c\ub300 \ub9c8\uc774\ub108\uc2a4 \ubb34\ud55c\ub300\ub97c \uc81c\uacf5\ud558\ub294 \uacbd\uc6b0 \uc774\ub294 \ubd88\ud655\uc815\uc131(\ub610\ub294 \ubd88\ud655\uc815\ud615)\uc784\uc744 \uc758\ubbf8\ud569\ub2c8\ub2e4. \uc989 <strong>, \ubd88\ud655\uc815\uc131 &#8211; \ubb34\ud55c\ub300\ub97c \ubd80\uc5ec\ud558\ub294 \ud568\uc218\uc758 \uadf9\ud55c\uc740<\/strong> \uc9c1\uc811\uc801\uc778 \uacc4\uc0b0\uc744 \ud1b5\ud574\uc11c\ub294 \uacb0\uc815\ub420 \uc218 \uc5c6\uace0, \uc624\ud788\ub824 \uc0ac\uc804\uc801\uc778 \uacfc\uc815\uc744 \uac70\uccd0\uc57c \ud55c\ub2e4.<\/p>\n<p> \ub530\ub77c\uc11c <strong>\ubb34\ud55c \ub9c8\uc774\ub108\uc2a4 \ubb34\ud55c \ubd88\ud655\uc815\uc131\uc744 \ud480\ub824\uba74<\/strong> \uba3c\uc800 \ud568\uc218 \uc720\ud615\uc5d0 \ub530\ub77c \ub2ec\ub77c\uc9c0\ub294 \uc808\ucc28\ub97c \uc801\uc6a9\ud574\uc57c \ud569\ub2c8\ub2e4. \ub2e4\ud56d \ud568\uc218\uc778 \uacbd\uc6b0 \ube44\uad50\ub97c \ud1b5\ud574 \uacc4\uc0b0\ud560 \uc218 \uc788\uace0, \uc720\ub9ac \ud568\uc218\uc778 \uacbd\uc6b0 \ubd84\uc218\ub97c \ub2e4\uc74c\uc73c\ub85c \uc904\uc5ec\uc57c \ud569\ub2c8\ub2e4. \uacf5\ud1b5\ubd84\ubaa8\uc774\uba70, \ubb34\ub9ac\ud568\uc218\uc778 \uacbd\uc6b0 \uacf5\uc561\uc744 \uacf1\ud574\uc57c \ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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> \ub2e4\uc74c\uc73c\ub85c, \uac01 \uc720\ud615\uc758 \ud568\uc218\uc5d0\uc11c \ubd88\ud655\uc815\uc131 \ubb34\ud55c &#8211; \ubb34\ud55c\uc774 \uc5b4\ub5bb\uac8c \ud574\uacb0\ub418\ub294\uc9c0 \uc608\ub97c \ud1b5\ud574 \uc0b4\ud3b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-infinito-menos-infinito-en-funciones-polinomicas\"><\/span> \ub2e4\ud56d\uc2dd \ud568\uc218\uc758 \ubb34\ud55c \ub9c8\uc774\ub108\uc2a4 \ubb34\ud55c \ubd88\ud655\uc815\uc131 <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\">\n<p style=\"text-align:left\"> \ub2e4\ud56d\uc2dd\uc5d0\uc11c \ubd88\ud655\uc815\uc131 \ubb34\ud55c\ub300 \ube7c\uae30 \ubb34\ud55c\ub300\ub294 \ucd5c\uace0 \ucc28\uc218 \ubb34\ud55c\ub300\uc640 \uac19\uc2b5\ub2c8\ub2e4. \uc989, \ucd5c\uace0 \ucc28\uc218 \ud56d\uc774 \ubb34\ud55c\ub300\uc758 \uc591\uc218 \ub610\ub294 \uc74c\uc218 \ubd80\ud638\ub97c \uacb0\uc815\ud569\ub2c8\ub2e4.<\/p>\n<\/div>\n<p> \uc608\ub97c \ub4e4\uc5b4, \ubb34\ud55c\ub300\uc5d0\uc11c \ubb34\ud55c\ub300\ub97c \ube80 \ubd88\ud655\uc815 \ud615\uc2dd\uc744 \uc81c\uacf5\ud558\ub294 \ub2e4\uc74c \ub2e4\ud56d\uc2dd \ud568\uc218\uc758 \uadf9\ud55c\uc744 \uc0b4\ud3b4\ubcf4\uc138\uc694.<\/p>\n<\/p>\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> \uc774 \uacbd\uc6b0 x <sup>2<\/sup> \ud56d\uc740 2\ucc28\uc774\uace0 3x \ud56d\uc740 1\ucc28\uc774\ubbc0\ub85c \ub2e8\ud56d\uc2dd x <sup>2<\/sup> \uac00 \ub354 \ub192\uc740 \ucc28\uc218\uc774\uae30 \ub54c\ubb38\uc5d0 \uc6b0\uc138\ud569\ub2c8\ub2e4. \ub530\ub77c\uc11c \uadf9\ud55c\uc758 \uacb0\uacfc\ub294 \uc774 \ud56d\uc5d0\uc11c \uc5bb\uc5b4\uc9c0\ub294 \ubb34\ud55c\ub300\uc785\ub2c8\ub2e4.<\/p>\n<p> \ub2e4\uc74c\uc758 \ub2e4\ub978 \uc608\ub97c \uc0b4\ud3b4\ubcf4\uc138\uc694.<\/p>\n<\/p>\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> \uac04\ub2e8\ud788 \ub9d0\ud574\uc11c, \ub2e4\ud56d\uc2dd \ud568\uc218\uc5d0\uc11c \ubb34\ud55c\ub300\uc5d0 \ub300\ud55c \uc81c\ud55c\uc744 \ub9cc\ub4e4 \ub54c \ub2e4\ub978 \ubaa8\ub4e0 \ud56d\uc744 \ubb34\uc2dc <strong>\ud558\uace0 \ub2e8\uc21c\ud788 \ucd5c\uace0\ucc28 \ud56d\uc5d0 \ubb34\ud55c\ub300\ub97c \ub300\uccb4\ud574\uc57c \ud569\ub2c8\ub2e4<\/strong> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-infinito-menos-infinito-con-fracciones\"><\/span> \ubd88\ud655\uc815\uc131 \ubb34\ud55c &#8211; \ubd84\uc218 \ud3ec\ud568 \ubb34\ud55c <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\">\n<p style=\"text-align:left\"> <strong>\ub300\uc218 \ubd84\uc218\uc758 \ub367\uc148\uc774\ub098 \ube84\uc148\uc5d0\uc11c \ubd88\ud655\uc815\uc131 \ubb34\ud55c\ub300 \ube7c\uae30 \ubb34\ud55c\ub300\uac00 \ubc1c\uc0dd<\/strong> \ud558\uba74 \uba3c\uc800 \ubd84\uc218\uc758 \ub367\uc148\uc774\ub098 \ube84\uc148\uc744 \ud55c \ub2e4\uc74c \uadf9\ud55c\uc744 \uacc4\uc0b0\ud574\uc57c \ud569\ub2c8\ub2e4.<\/p>\n<\/div>\n<p> \uc608\uc81c\ub97c \ub2e8\uacc4\ubcc4\ub85c \ud480\uc5b4 \ubd84\uc218\uac00 \uc788\ub294 \ud568\uc218\uc5d0\uc11c \ubd88\ud655\uc815\uc131 \ubb34\ud55c\ub300 \ube7c\uae30 \ubb34\ud55c\ub300\ub97c \uacc4\uc0b0\ud558\ub294 \ubc29\ubc95\uc744 \uc0b4\ud3b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n<\/p>\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> \uba3c\uc800 \ud55c\ub3c4\ub97c \uacc4\uc0b0\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n<\/p>\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> \uadf8\ub7ec\ub098 \uc6b0\ub9ac\ub294 \ubd88\ud655\uc815\uc131 -0\uc744 \uc5bb\uc2b5\ub2c8\ub2e4.<\/p>\n<p> \uba3c\uc800 \ubd84\uc218\uc758 \ube84\uc148\uc744 \ud574\uc57c \ud569\ub2c8\ub2e4. \uc774\ub97c \uc704\ud574 \ubd84\uc218\ub97c \uacf5\ud1b5 \ubd84\ubaa8\ub85c \uc904\uc785\ub2c8\ub2e4. \uc989, \ud55c \ubd84\uc218\uc758 \ubd84\uc790\uc640 \ubd84\ubaa8\uc5d0 \ub2e4\ub978 \ubd84\uc218\uc758 \ubd84\ubaa8\ub97c \uacf1\ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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> \uc774\uc81c \ub450 \ubd84\uc218\uc758 \ubd84\ubaa8\uac00 \ub3d9\uc77c\ud558\ubbc0\ub85c \uc774\ub97c \ud558\ub098\uc758 \ubd84\uc218\ub85c \uacb0\ud569\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n<\/p>\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> \ubd84\uc790\uc640 \ubd84\ubaa8\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc791\uc5c5\ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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> \ub9c8\uc9c0\ub9c9\uc73c\ub85c \ud55c\uacc4\ub97c \ub2e4\uc2dc \uacc4\uc0b0\ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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> \uc774 \uacbd\uc6b0, \ubd84\uc790\uc758 \ucc28\uc218\uac00 \ubd84\ubaa8\uc758 \ucc28\uc218\ubcf4\ub2e4 \ud06c\uae30 \ub54c\ubb38\uc5d0 \ubb34\ud55c\ub300 \uc0ac\uc774\uc758 \ubb34\ud55c \ubd88\ud655\uc815\uc131\uc740 +\ubb34\ud55c\ub300\ub97c \uc81c\uacf5\ud569\ub2c8\ub2e4.<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\ucc38\uace0:<\/strong> <a href=\"https:\/\/mathority.org\/ko\/\u1106\u116e\u1112\u1161\u11ab-\u1109\u1161\u110b\u1175\u110b\u1174-\u1107\u116e\u11af\u1112\u116a\u11a8\u110c\u1165\u11bc-\u1106\u116e\u1112\u1161\u11ab-%e2%88%9e-%e2%88%9e\/\"><span style=\"text-decoration: underline;\">\ubb34\ud55c\ub300 \uc0ac\uc774\uc758 \ubb34\ud55c\ub300\ub294 \ubb34\uc5c7\uc778\uac00\uc694?<\/span><\/a> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-infinito-menos-infinito-con-raices\"><\/span> \ubd88\ud655\uc815\uc131 \ubb34\ud55c &#8211; \ubfcc\ub9ac\uac00 \uc788\ub294 \ubb34\ud55c <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\">\n<p style=\"text-align:left\"> <strong>\ubd88\ud655\uc815\uc131 \ubb34\ud55c\ub300 \ube7c\uae30 \ubb34\ud55c\ub300\uac00 \uadfc\uc218 \ub367\uc148 \ub610\ub294 \ube84\uc148\uc5d0\uc11c \ubc1c\uc0dd\ud558\ub294<\/strong> \uacbd\uc6b0 \uba3c\uc800 \ud568\uc218\ub97c \ucf24\ub808 \uadfc\uc218 \ud45c\ud604\uc2dd\uc73c\ub85c \uacf1\ud558\uace0 \ub098\ub208 \ub2e4\uc74c \uadf9\ud55c\uc744 \ud480\uc5b4\uc57c \ud569\ub2c8\ub2e4.<\/p>\n<\/div>\n<p> \ub2e8\uacc4\ubcc4 \uc608\uc81c\ub97c \uc0ac\uc6a9\ud558\uc5ec \ube44\ud569\ub9ac \ud568\uc218\uc5d0\uc11c \ubd88\ud655\uc815\uc131 \ubb34\ud55c &#8211; \ubb34\ud55c\uc744 \ud574\uacb0\ud558\ub294 \ubc29\ubc95\uc744 \uc0b4\ud3b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n<\/p>\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> \uba3c\uc800 \uadfc\ud638\ub97c \uc0ac\uc6a9\ud558\uc5ec \ud568\uc218\uc758 \uadf9\ud55c\uc744 \ud574\uacb0\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n<\/p>\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> \uadf8\ub7ec\ub098 \uc6b0\ub9ac\ub294 \ubd88\ud655\uc815 \ud615\ud0dc -0\uc744 \uc5bb\uc2b5\ub2c8\ub2e4. \ub530\ub77c\uc11c \ubb34\ud55c\ub300\uc5d0\uc11c \ubb34\ud55c\ub300\ub97c \ube80 \uac12\uc774 \uc5bc\ub9c8\ub098 \ud070\uc9c0 \uc54c\ub824\uba74 \uc124\uba85\ub41c \uc808\ucc28\ub97c \uc801\uc6a9\ud574\uc57c \ud569\ub2c8\ub2e4.<\/p>\n<p> \ud568\uc218\uc5d0 \uadfc\ud638\uac00 \uc788\uc73c\ubbc0\ub85c \uc804\uccb4 \ud568\uc218\ub97c \uacf5\uc561 \ubb34\ub9ac\uc218 \ud45c\ud604\uc2dd\uc73c\ub85c \uacf1\ud558\uace0 \ub098\ub215\ub2c8\ub2e4.<\/p>\n<\/p>\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> \ubd84\uc790\uc758 \ub300\uc218\uc801 \ud45c\ud604\uc740 \ucc28\uc774\uc5d0 \uc758\ud55c \ud569\uc758 \uacf1\uc758 \uc8fc\ubaa9\ud560\ub9cc\ud55c \ub3d9\uc77c\uc131\uc5d0 \ud574\ub2f9\ud558\ubbc0\ub85c \ud45c\ud604\uc744 \ub2e8\uc21c\ud654\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n<\/p>\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> \uc774\uc81c \uadf9\ud55c\uc774 \uc81c\uacf1\ub418\uc5c8\uc73c\ubbc0\ub85c \uadf9\ud55c\uc758 \uadfc\uc744 \ub2e8\uc21c\ud654\ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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> \uc6b0\ub9ac\ub294 \ubd84\uc218\uc758 \ubd84\uc790\uc5d0 \ub300\ud574 \uc5f0\uc0b0\uc744 \uc218\ud589\ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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 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> \ub9c8\uc9c0\ub9c9\uc73c\ub85c \ud55c\uacc4 \uacc4\uc0b0\uc744 \ub2e4\uc2dc \uc2e4\ud589\ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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> \ub530\ub77c\uc11c \uadf9\ud55c\uc758 \uacb0\uacfc\ub294 0\uc785\ub2c8\ub2e4. \uc65c\ub0d0\ud558\uba74 \ubb34\ud55c\ub300\ub85c \ub098\ub208 \ubaa8\ub4e0 \uc22b\uc790\ub294 0\uacfc \uac19\uae30 \ub54c\ubb38\uc785\ub2c8\ub2e4. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-indeterminacion-infinito-menos-infinito\"><\/span> \ubb34\ud55c \ub9c8\uc774\ub108\uc2a4 \ubb34\ud55c \ubd88\ud655\uc815\uc131 \ubb38\uc81c \ud574\uacb0<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> \uc5f0\uc2b5 1<\/h3>\n<p> x\uac00 \ub354\ud558\uae30 \ubb34\ud55c\ub300\uc5d0 \uc811\uadfc\ud560 \ub54c \ub2e4\uc74c \uadf9\ud55c\uc744 \ud574\uacb0\ud569\ub2c8\ub2e4. <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\ud574\uacb0\ucc45 \ubcf4\uae30<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \uc774 \uadf9\ud55c\uc5d0\uc11c \ucd5c\uace0\ucc28 \ud56d\uc740 3\ucc28\uc774\ubbc0\ub85c \uc774 \ud56d\uc5d0\uc11c \uc5bb\uc740 \ubb34\ud55c\ub300\uc5d0 \uc911\uc810\uc744 \ub461\ub2c8\ub2e4. <\/p>\n<\/p>\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\"><\/div>\n<h3 class=\"wp-block-heading\">\uc5f0\uc2b5 2<\/h3>\n<p> x\uac00 \uc74c\uc758 \ubb34\ud55c\ub300\uc5d0 \uc811\uadfc\ud560 \ub54c \ub2e4\uc74c \ub2e4\ud56d\uc2dd \ud568\uc218\uc758 \uadf9\ud55c\uc744 \uacc4\uc0b0\ud569\ub2c8\ub2e4. <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\ud574\uacb0\ucc45 \ubcf4\uae30<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \uc74c\uc758 \ubb34\ud55c\ub300 \uc138\uc81c\uacf1\uc740 \uc74c\uc218\ub85c \uc720\uc9c0\ub418\uc9c0\ub9cc \uc81c\uacf1\ud558\uba74 \uc591\uc218\uac00 \ub429\ub2c8\ub2e4. \ub098\uc911\uc5d0 \uadf8 \ubd80\ud638\ub294 \uc55e\uc5d0 \uc788\ub294 \uacc4\uc218\uc5d0 \uc758\ud574 \uc218\uc815\ub418\uc9c0\ub9cc:<\/p>\n<\/p>\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\"> \uadf8\ub7f0 \ub2e4\uc74c, \ubb34\ud55c\ub300 \ub9c8\uc774\ub108\uc2a4 \ubb34\ud55c\ub300 \ud615\ud0dc\uc758 \ubd80\uc815\ud615\uc740 \ucc28\uc218\uac00 \uac00\uc7a5 \ub192\uc740 \ud56d(-5x <sup>3<\/sup> )\uc73c\ub85c \uc815\uc758\ub418\uba70, \uc5ec\uae30\uc5d0\uc11c \uc591\uc758 \ubb34\ud55c\ub300\ub97c \uc5bb\uc2b5\ub2c8\ub2e4. <\/p>\n<\/p>\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\"><\/div>\n<h3 class=\"wp-block-heading\">\uc5f0\uc2b5 3<\/h3>\n<p> \ub2e4\uc74c \uc720\ub9ac \ud568\uc218\uc758 \ubb34\ud55c\ub300 \uadf9\ud55c\uc744 \uacb0\uc815\ud569\ub2c8\ub2e4. <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\ud574\uacb0\ucc45 \ubcf4\uae30<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \uba3c\uc800, \ud568\uc218\uc758 \ubb34\ud55c\ub300\ub97c \ub300\uccb4\ud558\uc5ec \uadf9\ud55c\uc744 \uacc4\uc0b0\ud558\ub824\uace0 \ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uadf8\ub7ec\ub098 \uc6b0\ub9ac\ub294 \ubd88\ud655\uc815\uc131 &#8211; \ub85c \ub05d\ub0a9\ub2c8\ub2e4. \ub530\ub77c\uc11c \ubd84\uc218\ub97c \uacf5\ud1b5 \ubd84\ubaa8\ub85c \uc904\uc785\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uc774\uc81c \ub450 \ubd84\uc218\uc758 \ubd84\ubaa8\uac00 \ub3d9\uc77c\ud558\ubbc0\ub85c \uc774\ub97c \ud558\ub098\uc758 \ubd84\uc218\ub85c \uacb0\ud569\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \ubd84\uc790\uc5d0 \uad04\ud638\ub97c \ub9cc\ub4ed\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uadf8\ub9ac\uace0 \ub9c8\uc9c0\ub9c9\uc73c\ub85c \ud55c\uacc4\ub97c \uacb0\uc815\ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uc774 \uacbd\uc6b0, \ubd84\uc790\uc758 \ucc28\uc218\ub294 \ubd84\ubaa8\uc758 \ucc28\uc218\ubcf4\ub2e4 \ud06c\uae30 \ub54c\ubb38\uc5d0 \ubd88\ud655\uc815 \/0\ub294 + \ub97c \uc81c\uacf5\ud569\ub2c8\ub2e4.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> \uc5f0\uc2b5 4<\/h3>\n<p> x\uac00 0\uc5d0 \uac00\uae4c\uc6cc\uc9c8 \ub54c \ub2e4\uc74c \ubd84\uc218 \ud568\uc218\uc758 \uadf9\ud55c\uc744 \ud489\ub2c8\ub2e4. <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\ud574\uacb0\ucc45 \ubcf4\uae30<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \uba3c\uc800 \ud3c9\uc18c\uc640 \uac19\uc774 \ud55c\ub3c4\ub97c \uacc4\uc0b0\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uadf8\ub7ec\ub098 \uc6b0\ub9ac\ub294 \ubd88\ud655\uc815 \ud615\ud0dc\uc778 \ubb34\uc5c7\uc744 \uc5bb\uc2b5\ub2c8\uae4c? \ub530\ub77c\uc11c \ud568\uc218\uc758 \ubd84\uc218\ub97c \uacf5\ud1b5 \ubd84\ubaa8\ub85c \uc904\uc5ec\uc57c \ud569\ub2c8\ub2e4.<\/p>\n<p class=\"has-text-align-left\"> \uc774 \uacbd\uc6b0 x <sup>4<\/sup> \ub294 x <sup>2<\/sup> \uc758 \ubc30\uc218\uc774\ubbc0\ub85c \ub450 \ubc88\uc9f8 \ubd84\uc218\uc758 \ubd84\uc790\uc640 \ubd84\ubaa8\uc5d0 x <sup>2<\/sup> \ub97c \uacf1\ud558\uba74 \ub450 \ubd84\uc218\uc758 \ubd84\ubaa8\uac00 \ub3d9\uc77c\ud558\ub2e4\ub294 \uac83\uc744 \uc54c \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uc774\uc81c \ub450 \ubd84\uc218\ub97c \ube84 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uc6b0\ub9ac\ub294 \ud55c\ub3c4\ub97c \ub2e4\uc2dc \ud574\uacb0\ud558\ub824\uace0 \uc2dc\ub3c4\ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uadf8\ub7ec\ub098 \uc6b0\ub9ac\ub294 0\uc73c\ub85c \ub098\ub208 \uc0c1\uc218\uc758 \ubd88\ud655\uc815\uc131\uc73c\ub85c \ub05d\ub0a9\ub2c8\ub2e4. \ub530\ub77c\uc11c \ud568\uc218\uc758 \uce21\uba74 \ud55c\uacc4\ub97c \uacc4\uc0b0\ud558\ub294 \uac83\uc774 \ud544\uc694\ud569\ub2c8\ub2e4. <\/p>\n<\/p>\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 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\"> \uacb0\ub860\uc801\uc73c\ub85c, \uc810 x=0\uc5d0\uc11c \ud568\uc218\uc758 \ub450 \uce21\uba74 \uadf9\ud55c\uc740 -\ubb34\ud55c\uc744 \uc81c\uacf5\ud558\ubbc0\ub85c \uadf9\ud55c\uc758 \ud574\ub294 -\ubb34\ud55c\uc785\ub2c8\ub2e4. <\/p>\n<\/p>\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\"><\/div>\n<h3 class=\"wp-block-heading\">\uc5f0\uc2b5 5<\/h3>\n<p> \uadfc\uc744 \uc0ac\uc6a9\ud558\uc5ec \ub2e4\uc74c \ud568\uc218\uc758 \ubb34\ud55c\ub300 \uadf9\ud55c\uc744 \ud489\ub2c8\ub2e4. <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\ud574\uacb0\ucc45 \ubcf4\uae30<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \uadf9\ud55c\uc744 \ud480\ub824\uace0 \uc2dc\ub3c4\ud558\uba74 \ubd88\ud655\uc815\uc131 \ubb34\ud55c\ub300 \ub9c8\uc774\ub108\uc2a4 \ubb34\ud55c\ub300\ub97c \uc5bb\uc2b5\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \ub530\ub77c\uc11c \ud568\uc218\uc5d0 \uadfc\ud638\uac00 \uc788\uc73c\ubbc0\ub85c \uc774\ub97c \uacf5\uc561 \uadfc\ud638 \ud45c\ud604\uc73c\ub85c \uacf1\ud558\uace0 \ub098\ub204\uc5b4\uc57c \ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \ubd84\uc790\uc5d0\ub294 \uc81c\uacf1\uc758 \ucc28\uc774\uc640 \ub3d9\uc77c\ud55c \ucc28\uc774\uc5d0 \uc758\ud55c \ud569\uc758 \uacf1\uc774 \uc788\uc2b5\ub2c8\ub2e4. \uc544\uc9c1:<\/p>\n<\/p>\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\"> \uadfc\ud638\ub97c \uc81c\uacf1\uc73c\ub85c \ub2e8\uc21c\ud654\ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uc6b0\ub9ac\ub294 \ubd84\uc790\uc5d0\uc11c \uc791\ub3d9\ud569\ub2c8\ub2e4: <\/p>\n<\/p>\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 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\"> \uadf8\ub9ac\uace0 \ub9c8\uc9c0\ub9c9\uc73c\ub85c \ud55c\uacc4\ub97c \ucc3e\uc558\uc2b5\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uc774 \uacbd\uc6b0 \ubb34\ud55c \ubd88\ud655\uc815\uc131\uc744 \ubb34\ud55c\ub300\ub85c \ub098\ub208 \uac12\uc740 \ubd84\uc790\uc758 \ucc28\uc218\uac00 \ubd84\ubaa8\uc758 \ucc28\uc218\ubcf4\ub2e4 \ud06c\uae30 \ub54c\ubb38\uc5d0 \ub354 \ubb34\ud55c\ud569\ub2c8\ub2e4(\uc81c\uacf1\uadfc\uc740 \ucc28\uc218\ub97c 2\ub85c \uc904\uc778\ub2e4\ub294 \uc810\uc744 \uae30\uc5b5\ud558\uc138\uc694:<\/p>\n<\/p>\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\"><\/div>\n<h3 class=\"wp-block-heading\"> \uc5f0\uc2b5 6<\/h3>\n<p> x\uac00 \ub2e4\uc74c \ubb34\ub9ac \ud568\uc218\uc758 \ubb34\ud55c\ub300\uc5d0 \uc811\uadfc\ud560 \ub54c \uadf9\ud55c\uc744 \ud489\ub2c8\ub2e4. <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\ud574\uacb0\ucc45 \ubcf4\uae30<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \uba3c\uc800 \ud3c9\uc18c\uc640 \uac19\uc774 \ud55c\ub3c4\ub97c \uacc4\uc0b0\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uadf8\ub7ec\ub098 \uadf8\uac83\uc740 \uacb0\uacfc\uc801\uc73c\ub85c \ubb34\ud55c\ub300\uc758 \ucc28\uc774\ub97c \ubd88\ud655\uc815\ud558\uac8c \ub9cc\ub4ed\ub2c8\ub2e4. \ub530\ub77c\uc11c \ud568\uc218\uc5d0 \uadfc\uc774 \uc788\uc73c\ubbc0\ub85c \ud45c\ud604\uc2dd\uc744 \uacf5\uc561\uadfc\uc218\ub85c \uacf1\ud558\uace0 \ub098\ub204\uc5b4\uc57c \ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uc6b0\ub9ac\ub294 \ubd84\uc218 \ubd84\uc790\uc758 \ub208\uc5d0 \ub744\ub294 \ub3d9\ub4f1\uc131\uc744 \uadf8\ub8f9\ud654\ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uc6b0\ub9ac\ub294 \uc81c\uacf1\uadfc\uc744 \ud47c\ub2e4:<\/p>\n<\/p>\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\"> \uc6b0\ub9ac\ub294 \ucc28\uc774\uc758 \uc81c\uacf1\uc5d0 \ub300\ud55c \uc8fc\ubaa9\ud560 \ub9cc\ud55c \ud56d\ub4f1\uc2dd\uc744 \ud574\uacb0\ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uc6b0\ub9ac\ub294 \ubd84\uc790\uc5d0\uc11c \uc791\ub3d9\ud569\ub2c8\ub2e4: <\/p>\n<\/p>\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 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\"> \uadf8\ub9ac\uace0 \ub9c8\uc9c0\ub9c9\uc73c\ub85c \ubb34\ud55c\ub300\uc758 \uadf9\ud55c \uac12\uc744 \uacc4\uc0b0\ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \ubd84\ubaa8\uc5d0 x \uc81c\uacf1\uc774 \uc788\ub354\ub77c\ub3c4 \ub8e8\ud2b8 \uc548\uc5d0 \uc788\uae30 \ub54c\ubb38\uc5d0 \ucc28\uc218\ub294 \uc2e4\uc81c\ub85c 1\uc785\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \ub530\ub77c\uc11c, \ubd88\ud655\uc815\uc131 -\ubb34\ud55c\ub300\/+\ubb34\uc758 \uacb0\uacfc\ub294 \ubd84\uc790\uc758 \ucc28\uc218\uac00 \ubd84\ubaa8\uc758 \ucc28\uc218\uc640 \ub3d9\uc77c\ud558\uae30 \ub54c\ubb38\uc5d0 \ub354 \ub192\uc740 \ucc28\uc218\uc778 x\uc758 \uacc4\uc218\ub97c \ub098\ub208 \uac83\uc785\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \ubd84\ubaa8\uc5d0\ub294 2\uac1c\uc758 1\ucc28 \ud56d\uc774 \uc788\uc73c\ubbc0\ub85c \uc8fc\uc758\ud558\uc138\uc694.<\/p>\n<\/p>\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> \uadf8\ub9ac\uace0<\/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> , \ubd88\ud655\uc815\uc131 -\ubb34\ud55c\ub300\/+\ubb34\ub300\ub97c \ud574\uacb0\ud558\ub824\uba74 1\ucc28 \ud56d\uc758 \ubaa8\ub4e0 \uacc4\uc218\ub97c \ucde8\ud574\uc57c \ud569\ub2c8\ub2e4. \uc989<\/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> ~\uc758<\/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> \uadf8\ub9ac\uace0<\/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> ~\uc758 <\/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\"><\/div>\n<h3 class=\"wp-block-heading\">\uc5f0\uc2b5 7<\/h3>\n<p> x\uac00 \ubd84\uc218\ub97c \uc0ac\uc6a9\ud558\uc5ec \ub2e4\uc74c \ud568\uc218 \uc911 1\uc5d0 \uc811\uadfc\ud560 \ub54c \uadf9\ud55c\uc744 \uacc4\uc0b0\ud569\ub2c8\ub2e4. <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\ud574\uacb0\ucc45 \ubcf4\uae30<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \uadf9\ud55c\uc744 \ub9cc\ub4e4\ub824\uace0 \ud558\uba74 \ubb34\ud55c\ub300\uc5d0\uc11c \ubb34\ud55c\ub300\ub97c \ube80 \ubd88\ud655\uc815 \uadf9\ud55c\uc744 \uc5bb\uac8c \ub429\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \ub530\ub77c\uc11c \ubd84\uc218\ub97c \uacf5\ud1b5 \ubd84\ubaa8\ub85c \uc904\uc5ec\uc57c \ud569\ub2c8\ub2e4. \uc989, \ud55c \ubd84\uc218\uc758 \ubd84\uc790\uc640 \ubd84\ubaa8\uc5d0 \ub2e4\ub978 \ubd84\uc218\uc758 \ubd84\ubaa8\ub97c \uacf1\ud574\uc57c \ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uadf8\ub9ac\uace0 \uc774\uc81c \ub450 \ubd84\uc218\uc758 \ubd84\ubaa8\uac00 \uac19\uc73c\ubbc0\ub85c \ud569\uce60 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uc6b0\ub9ac\ub294 \ub2e4\uc74c\uc744 \uc6b4\uc601\ud569\ub2c8\ub2e4: <\/p>\n<\/p>\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 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\"> \uadf8\ub9ac\uace0 \uc6b0\ub9ac\ub294 \ub2e4\uc2dc \ud55c \ubc88 \ud55c\uacc4\ub97c \ud574\uacb0\ud558\ub824\uace0 \ub178\ub825\ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uadf8\ub7ec\ub098 \uc6b0\ub9ac\ub294 \ubd88\ud655\uc815\uc131 0\uc744 0\uc73c\ub85c \ub098\ub208 \uac12\uc744 \ucc3e\uc2b5\ub2c8\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \uc6b0\ub9ac\ub294 \ubd84\uc790\uc640 \ubd84\ubaa8 \ub2e4\ud56d\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud574\uc57c \ud569\ub2c8\ub2e4:<\/p>\n<\/p>\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\"> \uc774\uc81c \ubd84\uc790\uc640 \ubd84\ubaa8\uc5d0\uc11c \ubc18\ubcf5\ub418\ub294 \uc694\uc18c\ub97c \uc81c\uac70\ud558\uc5ec \ubd84\uc218\ub97c \ub2e8\uc21c\ud654\ud569\ub2c8\ub2e4.<\/p>\n<\/p>\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\"> \uadf8\ub9ac\uace0 \ub9c8\uc9c0\ub9c9\uc73c\ub85c \ud55c\uacc4\ub97c \ud574\uacb0\ud569\ub2c8\ub2e4. <\/p>\n<\/p>\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\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\uc774 \uae30\uc0ac\uc5d0\uc11c\ub294 \ubb34\ud55c \ube7c\uae30 \ubb34\ud55c(\ubb34\ud55c\ub300-\ubb34\ud55c\ub300) \ubd88\ud655\uc815\uc131\uc744 \ud574\uacb0\ud558\ub294 \ubc29\ubc95\uc744 \uc124\uba85\ud569\ub2c8\ub2e4. \ub2e4\uc591\ud55c \uc720\ud615\uc758 \ud568\uc218\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc774\ub7ec\ud55c \ubd88\ud655\uc815\uc131\uc758 \uc608\ub97c \ucc3e\uc744 \uc218 \uc788\uc73c\uba70, \ucd94\uac00\ub85c \ubd88\ud655\uc815\uc131 \ubb34\ud55c &#8211; \ubb34\ud55c\uc758 \ub2e8\uacc4\ubcc4 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \uc5f0\uc2b5\uc744 \ud1b5\ud574 \uc5f0\uc2b5\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \ubd88\ud655\uc815\uc131 \ubb34\ud55c \ub9c8\uc774\ub108\uc2a4 \ubb34\ud55c \ud480\uae30 \ud568\uc218\uc758 \uadf9\ud55c\uc774 \ubb34\ud55c\ub300 \ub9c8\uc774\ub108\uc2a4 \ubb34\ud55c\ub300\ub97c \uc81c\uacf5\ud558\ub294 \uacbd\uc6b0 \uc774\ub294 \ubd88\ud655\uc815\uc131(\ub610\ub294 \ubd88\ud655\uc815\ud615)\uc784\uc744 \uc758\ubbf8\ud569\ub2c8\ub2e4. \uc989 , \ubd88\ud655\uc815\uc131 &#8211; \ubb34\ud55c\ub300\ub97c \ubd80\uc5ec\ud558\ub294 \ud568\uc218\uc758 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ko\/%eb%b6%88%ed%99%95%ec%a0%95-%eb%ac%b4%ed%95%9c-%eb%a7%88%ec%9d%b4%eb%84%88%ec%8a%a4-%eb%ac%b4%ed%95%9c-%e2%88%9e-%e2%88%9e\/\"> <span class=\"screen-reader-text\">\ubd88\ud655\uc815\uc131 \ubb34\ud55c \ub9c8\uc774\ub108\uc2a4 \ubb34\ud55c(\ubb34\ud55c\ub300-\ubb34\ud55c\ub300)<\/span> \ub354 \ubcf4\uae30 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