{"id":6671,"date":"2021-07-20T23:48:52","date_gmt":"2021-07-20T14:48:52","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=6671"},"modified":"2021-07-21T18:17:15","modified_gmt":"2021-07-21T09:17:15","slug":"calculating-limits","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-calculus\/calculating-limits\/","title":{"rendered":"\uc218\uc5f4\uc758 \uadf9\ud55c \uacf5\uc2dd"},"content":{"rendered":"<div class=\"box itc_intro\">\n<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 1\uc7a5 3\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; <span class=\"itc_viewcontents\">(<a href=\"..\/\">\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30<\/a>)<\/span><\/p>\n<\/div>\n<p>\uc218\uc5f4 \\(\\left\\{a_n\\right\\}\\)\uc758 \uadf9\ud55c\uc744 \uad6c\ud560 \ub54c \\(n\\)\uc774 \ucee4\uc9d0\uc5d0 \ub530\ub77c \uc218\uc5f4\uc758 \ud56d \\(a_n\\)\uc774 \uc5b4\ub5bb\uac8c \uc6c0\uc9c1\uc774\ub294\uc9c0 \uad00\ucc30\ud558\ub294 \ubc29\ubc95\uc740 \ud6a8\uc728\uc801\uc774\uc9c0 \uc54a\ub2e4. \uc774 \uc808\uc5d0\uc11c\ub294 \uc218\uc5f4\uc758 \uadf9\ud55c\uc744 \uc27d\uac8c \uad6c\ud560 \uc218 \uc788\ub294 \uacf5\uc2dd\uc744 \uc0b4\ud3b4\ubcf4\uc790.<\/p>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\uc0ac\uce59\uacc4\uc0b0\uacfc \uad00\ub828\ub41c \uadf9\ud55c\uc758 \uc131\uc9c8<\/h2>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 1.3.1.<\/span><br \/>\n\\(\\left\\{a_n\\right\\}\\)\uacfc \\(\\left\\{b_n\\right\\}\\)\uc774 \uc2e4\uc218\uc5f4\uc774\uace0 \\(A\\)\uc640 \\(B\\)\uac00 \uc2e4\uc218\ub77c\uace0 \ud558\uc790. \uadf8\ub9ac\uace0<br \/>\n\\[\\lim_{n\\rightarrow\\infty} a_n = A \\quad\\text{and}\\quad \\lim_{n\\rightarrow\\infty} b_n = B\\]<br \/>\n\ub77c\uace0 \uac00\uc815\ud558\uc790. \uadf8\ub7ec\uba74 \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ol class=\"bracket\">\n<li>\\(\\displaystyle\\lim_{n\\rightarrow\\infty}\\left(ka_n \\right) = kA.\\) &nbsp;&nbsp;(\\(k\\)\ub294 \uc2e4\uc218\uc778 \uc0c1\uc218.)<\/li>\n<li>\\(\\displaystyle\\lim_{n\\rightarrow\\infty}\\left(a_n + b_n \\right) = A+B.\\)<\/li>\n<li>\\(\\displaystyle\\lim_{n\\rightarrow\\infty}\\left(a_n &#8211; b_n \\right) = A-B.\\)<\/li>\n<li>\\(\\displaystyle\\lim_{n\\rightarrow\\infty}\\left(a_n \\cdot b_n \\right) = AB.\\)<\/li>\n<li>\\(\\displaystyle\\lim_{n\\rightarrow\\infty}\\frac{a_n}{b_n} = \\frac{A}{B}.\\) &nbsp;&nbsp;(\ub2e8, \\(B\\ne 0\\)\uc774\uace0, \uc784\uc758\uc758 \\(n\\)\uc5d0 \ub300\ud558\uc5ec \\(b_n \\ne 0.\\))<\/li>\n<li>\\(\\displaystyle\\lim_{n\\rightarrow\\infty}\\left( a_n \\right)^m = A^m .\\) &nbsp;&nbsp;(\\(m\\)\uc740 \uc591\uc758 \uc815\uc218.)<\/li>\n<li>\\(\\displaystyle\\lim_{n\\rightarrow\\infty}\\sqrt[m]{a_n} = \\sqrt[m]{A}.\\) &nbsp;&nbsp;(\ub2e8, \\(A\\ge 0\\)\uc774\uace0, \uc784\uc758\uc758 \\(n\\)\uc5d0 \ub300\ud558\uc5ec \\(a_n \\ge 0\\)\uc774\uba70, \\(m\\)\uc740 \uc591\uc758 \uc815\uc218.)<\/li>\n<\/ol>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n<p>\uc774 \uc815\ub9ac\ub97c \uc99d\uba85\ud558\ub824\uba74 \\(\\epsilon-N\\) \uc815\uc758\ub97c \uc0ac\uc6a9\ud574\uc57c \ud558\ubbc0\ub85c \uc774 \ucc45\uc5d0\uc11c\ub294 \uc99d\uba85\uc744 \uc0dd\ub7b5\ud55c\ub2e4. \uc5c4\ubc00\ud55c \uc99d\uba85\uc774 \uad81\uae08\ud558\ub2e4\uba74 \uc774 \ube14\ub85c\uadf8\uc758 \ud3ec\uc2a4\ud2b8 \u300c<a href=\"\/blog\/articles\/calculus-limit-of-a-sequence-introduction\">\uc218\uc5f4\uc758 \uadf9\ud55c<\/a>\u300d \uc815\ub9ac 4\ub97c \ucc38\uace0\ud558\uae30 \ubc14\ub780\ub2e4.<br \/>\n<span class=\"qed\"><\/span><\/p>\n<\/div>\n<style type=\"text\/css\">\nol.ex010301 li { margin-bottom: 2em; }\n<\/style>\n<div class=\"example\">\n<p><span class=\"example\">\ubcf4\uae30 1.3.1.<\/span><\/p>\n<ol class=\"parenthesis ex010301\">\n<li>\\[\\lim_{n\\rightarrow\\infty}\\left( 5+ \\frac{1}{3}\\right)<br \/>\n= \\lim_{n\\rightarrow\\infty} 5 + \\lim_{n\\rightarrow\\infty} \\frac{1}{n}<br \/>\n= 5+0 = 5.\\]<\/li>\n<li>\\[\\begin{align}\\lim_{n\\rightarrow\\infty}\\left(\\frac{1}{n} &#8211; \\frac{10}{n^2}\\right)<br \/>\n&#038;= \\lim_{n\\rightarrow\\infty}\\frac{1}{n} &#8211; 10\\cdot\\left(\\lim_{n\\rightarrow\\infty}\\frac{1}{n}\\right)\\left(\\lim_{n\\rightarrow\\infty}\\frac{1}{n}\\right) \\\\[5pt]<br \/>\n&#038;= 0-10\\times 0\\times 0 = 0.<br \/>\n\\end{align}\\]<\/li>\n<li>\\[\\begin{align} \\lim_{n\\rightarrow\\infty}\\left(1+\\frac{3}{n^2}\\right)\\left(4-\\frac{3}{n}\\right)<br \/>\n&#038;= \\lim_{n\\rightarrow\\infty}\\left(1+\\frac{3}{n^2}\\right)\\cdot \\lim_{n\\rightarrow\\infty}\\left(4-\\frac{3}{n}\\right) \\\\[5pt]<br \/>\n&#038;=\\left( \\lim_{n\\rightarrow\\infty} 1 + \\lim_{n\\rightarrow\\infty} \\frac{3}{n^2}\\right)\\left( \\lim_{n\\rightarrow\\infty} 4 &#8211; \\lim_{n\\rightarrow\\infty} \\frac{3}{n}\\right) \\\\[5pt]<br \/>\n&#038;= (1+0)\\times (4-0) = 4.<br \/>\n\\end{align}\\]<\/li>\n<li>\\[\\begin{align} \\lim_{n\\rightarrow\\infty} \\frac{2-\\frac{4}{n}}{5+\\frac{3}{n^2}}<br \/>\n&#038;= \\frac{\\displaystyle\\lim_{n\\rightarrow\\infty} 2 &#8211; \\lim_{n\\rightarrow\\infty} \\frac{4}{n}}{\\displaystyle\\lim_{n\\rightarrow\\infty} 5 + \\lim_{n\\rightarrow\\infty} \\frac{3}{n^2}} \\\\[5pt]<br \/>\n&#038;= \\frac{2-0}{5+0} = \\frac{2}{5}.<br \/>\n\\end{align}\\]<\/li>\n<li>\\[\\begin{align} \\lim_{n\\rightarrow\\infty}\\frac{n^2 -2n+3}{-2n^2 +4}<br \/>\n&#038;= \\lim_{n\\rightarrow\\infty}\\frac{1 &#8211; \\frac{2}{n} + \\frac{3}{n^2}}{-2 + \\frac{4}{n^2}} \\\\[5pt]<br \/>\n&#038;= \\frac{\\displaystyle\\lim_{n\\rightarrow\\infty} 1 &#8211; \\lim_{n\\rightarrow\\infty} \\frac{2}{n} + \\lim_{n\\rightarrow\\infty} \\frac{3}{n^2}}{\\displaystyle\\lim_{n\\rightarrow\\infty} (-2) + \\lim_{n\\rightarrow\\infty}\\frac{4}{n^2}} \\\\[5pt]<br \/>\n&#038;= \\frac{1-0+0}{-2+0} = -\\frac{1}{2}.<br \/>\n\\end{align}\\]<\/li>\n<li>\\[\\begin{align} \\lim_{n\\rightarrow\\infty}\\left(3-\\frac{1}{n^4}\\right)^5<br \/>\n&#038;= \\left\\{ \\lim_{n\\rightarrow\\infty} \\left( 3-\\frac{1}{n^4}\\right)\\right\\}^5 \\\\[5pt]<br \/>\n&#038;= (3-0)^5 = 3^5 = 273.<br \/>\n\\end{align}\\]<\/li>\n<li>\\[\\begin{align} \\lim_{n\\rightarrow\\infty}\\sqrt{2-\\frac{1}{n}}<br \/>\n&#038;= \\sqrt{\\lim_{n\\rightarrow\\infty}\\left(2-\\frac{1}{n}\\right)} \\\\[5pt]<br \/>\n&#038;= \\sqrt{2-0} = \\sqrt{2}.<br \/>\n\\end{align}\\]<\/li>\n<li>\\[\\begin{align} \\lim_{n\\rightarrow\\infty}\\left(\\frac{8n-1}{n+4}\\right)^{\\frac{2}{3}}<br \/>\n&#038;= \\lim_{n\\rightarrow\\infty} \\sqrt[3]{\\left(\\frac{8n-1}{n+4}\\right)^2} \\\\[5pt]<br \/>\n&#038;= \\sqrt[3]{ \\lim_{n\\rightarrow\\infty}\\left( \\frac{8n-1}{n+4}\\right)^2 } \\\\[5pt]<br \/>\n&#038;= \\sqrt[3]{\\left\\{\\lim_{n\\rightarrow\\infty}\\left(\\frac{8n-1}{n+4}\\right)\\right\\}^2} \\\\[5pt]<br \/>\n&#038;= \\left\\{ \\lim_{n\\rightarrow\\infty}\\left(\\frac{8n-1}{n+4}\\right) \\right\\}^{\\frac{2}{3}} =8^{\\frac{2}{3}} = 4.<br \/>\n\\end{align}\\]<\/li>\n<\/ol>\n<\/div>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\uc21c\uc11c\uad00\uacc4\uc640 \uad00\ub828\ub41c \uadf9\ud55c\uc758 \uc131\uc9c8<\/h2>\n<p>\ub450 \uc2e4\uc218\uc5f4 \\(\\left\\{a_n\\right\\}\\)\uacfc \\(\\left\\{b_n\\right\\}\\)\uc774 \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790. \ub9cc\uc57d \uc720\ud55c \uac1c\ub97c \uc81c\uc678\ud55c \ubaa8\ub4e0 \\(n\\)\uc5d0 \ub300\ud558\uc5ec \\(a_n \\le b_n\\)\uc774 \uc131\ub9bd\ud558\ub294 \uac83\uc744 \\(\\left\\{a_n\\right\\} \\le \\left\\{b_n\\right\\}\\)\uc73c\ub85c \ub098\ud0c0\ub0b8\ub2e4\uba74 \u2018\\(\\le\\)\u2019\ub294 \uc2e4\uc218\uc5f4\ub4e4\uc758 \ubaa8\uc784\uc5d0\uc11c \uc21c\uc11c\uad00\uacc4\uac00 \ub41c\ub2e4. [\ub2e8, \uc720\ud55c \uac1c\uc758 \ud56d\uc774 \uc11c\ub85c \ub2e4\ub978 \ub450 \uc218\uc5f4\uc744 \uac19\uc740 \uac83\uc73c\ub85c \uac04\uc8fc\ud588\uc744 \ub54c.] \ub2e4\uc74c \uc815\ub9ac\ub294 \uadf9\ud55c\uc774 \uc21c\uc11c\ub97c \ubcf4\uc874\ud558\ub294 \ubcc0\ud658\uc784\uc744 \uc124\uba85\ud55c\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 1.3.2.<\/span><br \/>\n\\(\\left\\{a_n\\right\\}\\)\uacfc \\(\\left\\{b_n\\right\\}\\)\uc774 \uc2e4\uc218\uc5f4\uc774\ub77c\uace0 \ud558\uc790. \uadf8\ub9ac\uace0 \uc720\ud55c \uac1c\ub97c \uc81c\uc678\ud55c \ubaa8\ub4e0 \\(n\\)\uc5d0 \ub300\ud558\uc5ec \\(a_n \\le b_n\\)\uc774\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ol class=\"bracket\">\n<li>\\(\\left\\{a_n\\right\\}\\)\uc774 \\(A\\)\uc5d0 \uc218\ub834\ud558\uace0 \\(\\left\\{b_n\\right\\}\\)\uc774 \\(B\\)\uc5d0 \uc218\ub834\ud558\uba74, \\(A\\le B\\)\uc774\ub2e4.<\/li>\n<li>\\(\\left\\{a_n\\right\\}\\)\uc774 \uc591\uc758 \ubb34\ud55c\ub300\uc5d0 \ubc1c\uc0b0\ud558\uba74 \\(\\left\\{b_n\\right\\}\\)\ub3c4 \uc591\uc758 \ubb34\ud55c\ub300\uc5d0 \ubc1c\uc0b0\ud55c\ub2e4.<\/li>\n<li>\\(\\left\\{b_n\\right\\}\\)\uc774 \uc74c\uc758 \ubb34\ud55c\ub300\uc5d0 \ubc1c\uc0b0\ud558\uba74 \\(\\left\\{a_n\\right\\}\\)\ub3c4 \uc74c\uc758 \ubb34\ud55c\ub300\uc5d0 \ubc1c\uc0b0\ud55c\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n<p>\uc774 \uc815\ub9ac\ub97c \uc99d\uba85\ud558\ub824\uba74 \\(\\epsilon-N\\) \uc815\uc758\ub97c \uc0ac\uc6a9\ud574\uc57c \ud558\ubbc0\ub85c \uc774 \ucc45\uc5d0\uc11c\ub294 \uc99d\uba85\uc744 \uc0dd\ub7b5\ud55c\ub2e4.<br \/>\n<span class=\"qed\"><\/span><\/p>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\uc608\uc81c 1.3.2.<\/span><br \/>\n\uc218\uc5f4 \\(\\left\\{ -2n^2 +n +1 \\right\\}\\)\uc758 \uadf9\ud55c\uc744 \uc870\uc0ac\ud558\uc2dc\uc624.<\/p>\n<p style=\"text-align: left;\"><span class=\"proof\">\ud480\uc774.<\/span><br \/>\n\\(n\\ge 2\\)\uc77c \ub54c \\(-2n^2 +n +1 \\le -n\\)\uc774\ub2e4.<br \/>\n\uadf8\ub7f0\ub370 \\(n\\rightarrow\\infty\\)\uc77c \ub54c \\(-n \\,\\rightarrow\\,-\\infty\\)\uc774\ubbc0\ub85c, \\(n\\rightarrow\\infty\\)\uc77c \ub54c \\(-2n^2 +n+1 \\,\\rightarrow\\,-\\infty\\)\uc774\ub2e4.\n<\/p>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\uc608\uc81c 1.3.3.<\/span><br \/>\n\ub2e4\uc74c \uc218\uc5f4\uc758 \uadf9\ud55c\uc744 \uc870\uc0ac\ud558\uc2dc\uc624.<br \/>\n\\[\\left\\{ \\frac{n^2 -2n-1}{n+1} \\right\\}\\]\n<\/p>\n<p style=\"text-align: left;\"><span class=\"proof\">\ud480\uc774.<\/span><br \/>\n\\(n\\)\uc774 \uc591\uc758 \uc815\uc218\uc77c \ub54c \ub2e4\uc74d\uc774 \uc131\ub9bd\ud55c\ub2e4.<br \/>\n\\[\\frac{n^2 -2n-1}{n+1} = \\frac{n-2-\\frac{1}{n}}{1+\\frac{1}{n}} \\ge \\frac{n-2-1}{2} = \\frac{1}{2}n &#8211; \\frac{3}{2}.\\]<br \/>\n\uadf8\ub7f0\ub370<br \/>\n\\[\\lim_{n\\rightarrow\\infty}\\left(\\frac{1}{2}n &#8211; \\frac{3}{2}\\right) = \\infty\\]<br \/>\n\uc774\ubbc0\ub85c<br \/>\n\\[\\lim_{n\\rightarrow\\infty}\\frac{n^2 -2n-1}{n+1} = \\infty\\]<br \/>\n\uc774\ub2e4.\n<\/p>\n<\/div>\n<p>\uadf9\ud55c\uc758 \uc21c\uc11c \ubcf4\uc874 \uc131\uc9c8\uc744 \uc138 \uac1c\uc758 \uc218\uc5f4\uc5d0 \uc801\uc6a9\ud558\uba74 \ub2e4\uc74c \uc815\ub9ac\ub97c \uc5bb\ub294\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 1.3.3. (\uc870\uc784 \uc815\ub9ac)<\/span><\/p>\n<p>\\(\\left\\{a_n\\right\\},\\) \\(\\left\\{b_n\\right\\},\\) \\(\\left\\{c_n\\right\\}\\)\uc774 \uc2e4\uc218\uc5f4\uc774\ub77c\uace0 \ud558\uc790. \uadf8\ub9ac\uace0 \uc720\ud55c \uac1c\ub97c \uc81c\uc678\ud55c \ubaa8\ub4e0 \\(n\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[a_n \\le b_n \\le c_n\\]<br \/>\n\uc774\ub77c\uace0 \ud558\uc790. \ub9cc\uc57d \\(\\left\\{a_n\\right\\}\\)\uacfc \\(\\left\\{c_n\\right\\}\\)\uc774 \uac19\uc740 \uac12 \\(L\\)\uc5d0 \uc218\ub834\ud558\uba74, \\(\\left\\{b_n\\right\\}\\)\ub3c4 \\(L\\)\uc5d0 \uc218\ub834\ud55c\ub2e4.\n<\/p>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n<p>\uc774 \uc815\ub9ac\ub97c \uc99d\uba85\ud558\ub824\uba74 \\(\\epsilon-N\\) \uc815\uc758\ub97c \uc0ac\uc6a9\ud574\uc57c \ud558\ubbc0\ub85c \uc774 \ucc45\uc5d0\uc11c\ub294 \uc99d\uba85\uc744 \uc0dd\ub7b5\ud55c\ub2e4. \uc5c4\ubc00\ud55c \uc99d\uba85\uc774 \uad81\uae08\ud558\ub2e4\uba74 \uc774 \ube14\ub85c\uadf8\uc758 \ud3ec\uc2a4\ud2b8 \u300c<a href=\"\/blog\/articles\/calculus-limit-of-a-sequence-introduction\">\uc218\uc5f4\uc758 \uadf9\ud55c<\/a>\u300d \uc815\ub9ac 5\ub97c \ucc38\uace0\ud558\uae30 \ubc14\ub780\ub2e4.<br \/>\n<span class=\"qed\"><\/span><\/p>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\uc608\uc81c 1.3.4.<\/span> \\(\\left\\{a_n\\right\\}\\)\uc774 \uc2e4\uc218\uc5f4\uc774\uace0, \\(n\\ge 7\\)\uc77c \ub54c<br \/>\n\\[\\frac{3n}{n+1} \\le a_n \\le \\frac{3n+2}{n+1}\\]<br \/>\n\uac00 \uc131\ub9bd\ud55c\ub2e4\uace0 \ud558\uc790. \uc774\ub54c \\(\\left\\{a_n\\right\\}\\)\uc758 \uadf9\ud55c\uc744 \uc870\uc0ac\ud558\uc2dc\uc624.<\/p>\n<p><span class=\"proof\">\ud480\uc774.<\/span> \ubd80\ub4f1\uc2dd\uc758 \uccab \uc2dd\uacfc \ub9c8\uc9c0\ub9c9 \uc2dd\uc758 \uadf9\ud55c\uc744 \uad6c\ud558\uba74<br \/>\n\\[\\lim_{n\\rightarrow\\infty}\\frac{3n}{n+1} = 3 \\quad\\text{and}\\quad \\lim_{n\\rightarrow\\infty}\\frac{3n+2}{n+1} = 3\\]<br \/>\n\uc774\ubbc0\ub85c, \uc870\uc784 \uc815\ub9ac\uc5d0 \uc758\ud558\uc5ec \\(\\left\\{a_n\\right\\}\\)\uc774 \\(3\\)\uc5d0 \uc218\ub834\ud55c\ub2e4.\n<\/p>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\uc608\uc81c 1.3.5.<\/span>\\(\\left\\{a_n\\right\\}\\)\uc774 \uc2e4\uc218\uc5f4\uc774\uace0, \uc591\uc758 \uc815\uc218 \\(n\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[n^2 +n -4 \\le n^2 a_n \\le n^2 +3n -5\\]<br \/>\n\uac00 \uc131\ub9bd\ud55c\ub2e4\uace0 \ud558\uc790. \uc774\ub54c \\(\\left\\{a_n\\right\\}\\)\uc758 \uadf9\ud55c\uc744 \uc870\uc0ac\ud558\uc2dc\uc624.<\/p>\n<p><span class=\"proof\">\ud480\uc774.<\/span> \ubd80\ub4f1\uc2dd\uc758 \uac01 \uc2dd\uc744 \\(n^2\\)\uc73c\ub85c \ub098\ub204\uba74 \ub2e4\uc74c\uc744 \uc5bb\ub294\ub2e4.<br \/>\n\\[\\frac{n^2 +n -4}{n^2} \\le a_n \\le {n^2 +3n-5}{n^2}.\\]<br \/>\n\uadf8\ub7f0\ub370<br \/>\n\\[\\lim_{n\\rightarrow\\infty} \\frac{n^2 +n-4}{n^2} = \\lim_{n\\rightarrow\\infty} \\frac{n^2 +3n-5}{n^2} = 1\\]<br \/>\n\uc774\ubbc0\ub85c, \uc870\uc784 \uc815\ub9ac\uc5d0 \uc758\ud558\uc5ec \\(\\left\\{a_n\\right\\}\\)\uc774 \\(1\\)\uc5d0 \uc218\ub834\ud55c\ub2e4.\n<\/p>\n<\/div>\n<p><!-- ##################################################################### --><br \/>\n<!--\n\n\n<h2 class=\"itc_h2\">\uc81c\ubaa9<\/h2>\n\n\n\n\n\n<p>.<\/p>\n\n\n\n\n\n<p>.<\/p>\n\n\n--><\/p>\n<p><!--\n\n\n\n<div class=\"theorem margintop2\">\n\n\n<p><span class=\"theorem\">\uc815\ub9ac 1.<\/span>\n\n\n<\/p>\n\n<\/div>\n\n\n\n\n\n<div class=\"proof\">\n\n\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n\n\n\n\n<p>\n\n<span class=\"qed\"><\/span><\/p>\n\n<\/div>\n\n\n\n\n########\n\n\n\n\n<div class=\"example\">\n\n\n<p><span class=\"example\">\ubcf4\uae30 1.<\/span>\n\n<\/p>\n\n<\/div>\n\n\n\n\n\n<h2 class=\"itc_h2\"><\/h2>\n\n\n\n--><\/p>\n<div style=\"display: none; visibility: hidden;\">\n\\[<br \/>\n\\newcommand{\\Hom}{{\\operatorname{Hom}}}<br \/>\n\\newcommand{\\Mat}{{\\operatorname{Mat}}}<br \/>\n\\newcommand{\\proj}{{\\operatorname{proj}}}<br \/>\n\\newcommand{\\adj}{{\\operatorname{adj}}}<br \/>\n\\]\n<\/div>\n<div class=\"box itc_prev_next_box\">\n<ul class=\"itc_ul\">\n<li class=\"itc_li_prev\">\uc55e\uc758 \uae00 : <a href=\"..\/limit-of-a-sequence\">\uc218\uc5f4\uc758 \uadf9\ud55c\uc758 \uc815\uc758<\/a><\/li>\n<li class=\"itc_li_next\">\ub2e4\uc74c \uae00 : <a href=\"..\/geometric-sequences\">\ub4f1\ube44\uc218\uc5f4\uc758 \uadf9\ud55c<\/a><\/li>\n<\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 1\uc7a5 3\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; (\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30) \uc218\uc5f4 \\(\\left\\{a_n\\right\\}\\)\uc758 \uadf9\ud55c\uc744 \uad6c\ud560 \ub54c \\(n\\)\uc774 \ucee4\uc9d0\uc5d0 \ub530\ub77c \uc218\uc5f4\uc758 \ud56d \\(a_n\\)\uc774 \uc5b4\ub5bb\uac8c \uc6c0\uc9c1\uc774\ub294\uc9c0 \uad00\ucc30\ud558\ub294 \ubc29\ubc95\uc740 \ud6a8\uc728\uc801\uc774\uc9c0 \uc54a\ub2e4. \uc774 \uc808\uc5d0\uc11c\ub294 \uc218\uc5f4\uc758 \uadf9\ud55c\uc744 \uc27d\uac8c \uad6c\ud560 \uc218 \uc788\ub294 \uacf5\uc2dd\uc744 \uc0b4\ud3b4\ubcf4\uc790. \uc0ac\uce59\uacc4\uc0b0\uacfc \uad00\ub828\ub41c \uadf9\ud55c\uc758 \uc131\uc9c8 \uc815\ub9ac 1.3.1. \\(\\left\\{a_n\\right\\}\\)\uacfc \\(\\left\\{b_n\\right\\}\\)\uc774 \uc2e4\uc218\uc5f4\uc774\uace0 \\(A\\)\uc640 \\(B\\)\uac00 \uc2e4\uc218\ub77c\uace0 \ud558\uc790. \uadf8\ub9ac\uace0 \\(\\lim_{n\\rightarrow\\infty} a_n = A \\,\\text{and}\\, \\lim_{n\\rightarrow\\infty} b_n = B\\) \ub77c\uace0 \uac00\uc815\ud558\uc790. \uadf8\ub7ec\uba74&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":6620,"menu_order":103,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"class_list":["post-6671","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6671","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=6671"}],"version-history":[{"count":27,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6671\/revisions"}],"predecessor-version":[{"id":6839,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6671\/revisions\/6839"}],"up":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6620"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=6671"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}