{"id":6697,"date":"2021-07-20T23:58:17","date_gmt":"2021-07-20T14:58:17","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=6697"},"modified":"2021-08-30T12:45:18","modified_gmt":"2021-08-30T03:45:18","slug":"limits-involving-infinity","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-calculus\/limits-involving-infinity\/","title":{"rendered":"\ubb34\ud55c\ub300\ub97c \ud3ec\ud568\ud55c \uadf9\ud55c"},"content":{"rendered":"<div class=\"box itc_intro\">\n<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 3\uc7a5 4\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>\uc9d1\ud569 \\(D\\)\uac00 \uc704\ub85c \uc720\uacc4\uac00 \uc544\ub2c8\ub77c\uace0 \ud558\uace0, \ud568\uc218 \\(f:D \\rightarrow \\mathbb{R}\\)\ub97c \uc0dd\uac01\ud558\uc790.<\/p>\n<p>\ub9cc\uc57d \\(x\\)\uac00 \\(D\\)\uc5d0 \uc18d\ud55c \uc0c1\ud0dc\ub85c \ubb34\ud55c\ud788 \ucee4\uc9c8 \ub54c \\(f(x)\\)\uac00 \ud558\ub098\uc758 \uac12 \\(L\\)\uc5d0 \ud55c \uc5c6\uc774 \uac00\uae4c\uc774 \ub2e4\uac00\uac04\ub2e4\uba74 \u201c\\(x\\rightarrow\\infty\\)\uc77c \ub54c \\(f(x)\\)\uac00 \\(L\\)\uc5d0 <span class=\"defined\">\uc218\ub834\ud55c\ub2e4<\/span>\u201d\ub77c\uace0 \ub9d0\ud55c\ub2e4. \uc774\ub54c \\(L\\)\uc744 <span class=\"defined\">\uc591\uc758 \ubb34\ud55c\ub300\uc5d0\uc11c \\(\\boldsymbol{f(x)}\\)\uc758 \uadf9\ud55c<\/span>\uc774\ub77c\uace0 \ubd80\ub974\uba70, \uc774 \uc0ac\uc2e4\uc744<br \/>\n\\[\\lim_{x\\rightarrow\\infty}f(x)=L\\]<br \/>\n\ub610\ub294<br \/>\n\\[f(x) \\rightarrow L \\quad\\text{as}\\quad x\\rightarrow\\infty\\]<br \/>\n\uc640 \uac19\uc774 \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n<p>\ub9cc\uc57d \\(x\\)\uac00 \\(D\\)\uc5d0 \uc18d\ud55c \uc0c1\ud0dc\ub85c \ubb34\ud55c\ud788 \ucee4\uc9c8 \ub54c \\(f(x)\\)\uac00 \ubb34\ud55c\ud788 \ucee4\uc9c0\uba74 \u201c\\(x\\rightarrow\\infty\\)\uc77c \ub54c \\(f(x)\\)\uac00 <span class=\"defined\">\uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud55c\ub2e4<\/span>\u201d\ub77c\uace0 \ub9d0\ud55c\ub2e4. \uc774 \uc0ac\uc2e4\uc744<br \/>\n\\[\\lim_{x\\rightarrow\\infty}f(x)=\\infty\\]<br \/>\n\ub610\ub294<br \/>\n\\[f(x) \\rightarrow \\infty \\quad\\text{as}\\quad x\\rightarrow\\infty\\]<br \/>\n\uc640 \uac19\uc774 \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n<p>\ub9cc\uc57d \\(x\\)\uac00 \\(D\\)\uc5d0 \uc18d\ud55c \uc0c1\ud0dc\ub85c \ubb34\ud55c\ud788 \ucee4\uc9c8 \ub54c \\(f(x)\\)\uac00 \ubb34\ud55c\ud788 \uc791\uc544\uc9c0\uba74 \u201c\\(x\\rightarrow\\infty\\)\uc77c \ub54c \\(f(x)\\)\uac00 <span class=\"defined\">\uc74c\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud55c\ub2e4<\/span>\u201d\ub77c\uace0 \ub9d0\ud55c\ub2e4. \uc774 \uc0ac\uc2e4\uc744<br \/>\n\\[\\lim_{x\\rightarrow\\infty}f(x)= -\\infty\\]<br \/>\n\ub610\ub294<br \/>\n\\[f(x) \\rightarrow -\\infty \\quad\\text{as}\\quad x\\rightarrow\\infty\\]<br \/>\n\uc640 \uac19\uc774 \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n<p>\\(f\\)\uc758 \uc815\uc758\uc5ed \\(D\\)\uac00 \uc544\ub798\ub85c \uc720\uacc4\uac00 \uc544\ub2cc \uacbd\uc6b0, \\(x \\rightarrow -\\infty\\)\uc778 \uadf9\ud55c\ub3c4 \ub9c8\ucc2c\uac00\uc9c0 \ubc29\ubc95\uc73c\ub85c \uc815\uc758\ud55c\ub2e4.<\/p>\n<style type=\"text\/css\">\ndiv.example ol li {\nmargin-bottom: 1em;\n}\n<\/style>\n<div class=\"example\">\n<p><span class=\"example\">\ubcf4\uae30 3.4.1.<\/span><\/p>\n<ol class=\"parenthesis\">\n<li>\ub9cc\uc57d \\(f(x) = \\frac{1}{x}\\)\uc774\uba74<br \/>\n\\[\\lim_{x\\rightarrow\\infty}f(x) = 0 \\quad\\text{and}\\quad \\lim_{x\\rightarrow -\\infty} f(x) =0\\]<br \/>\n\uc774\ub2e4.<\/li>\n<li>\ub9cc\uc57d \\(f(x) = \\lfloor x \\rfloor \\)\uc774\uba74<br \/>\n\\[\\lim_{x\\rightarrow\\infty}f(x) = \\infty \\quad\\text{and}\\quad \\lim_{x\\rightarrow -\\infty} f(x) = -\\infty\\]<br \/>\n\uc774\ub2e4.<\/li>\n<li>\ub9cc\uc57d \\(f(x) = e^x \\sin x\\)\uc774\uba74<br \/>\n\\[\\lim_{x\\rightarrow -\\infty}f(x) = 0\\]<br \/>\n\uc774\uba70, \\(x\\rightarrow -\\infty\\)\uc77c \ub54c \\(f(x)\\)\ub294 \uc9c4\ub3d9\ud55c\ub2e4.<\/li>\n<li>\ub9cc\uc57d \\(f(x) = \\ln x\\)\uc774\uba74<br \/>\n\\[\\lim_{x\\rightarrow\\infty}f(x) = \\infty\\]<br \/>\n\uc774\ub2e4. \\(x\\rightarrow -\\infty\\)\uc77c \ub54c \\(f(x)\\)\uc758 \uadf9\ud55c\uc740 \uc815\uc758\ub418\uc9c0 \uc54a\ub294\ub2e4. \uc65c\ub0d0\ud558\uba74 \uc790\uc5f0\ub85c\uadf8 \ud568\uc218\uc758 \uc815\uc758\uc5ed\uc774 \\((0,\\,\\infty )\\)\ub85c\uc11c \uc544\ub798\ub85c \uc720\uacc4\uc774\uae30 \ub54c\ubb38\uc774\ub2e4.<\/li>\n<li>\ub9cc\uc57d \\(f(x) = \\tan^{-1} x\\)\uc774\uba74<br \/>\n\\[\\lim_{x\\rightarrow\\infty}f(x) = \\frac{\\pi}{2} \\quad\\text{and}\\quad \\lim_{x\\rightarrow -\\infty} f(x) = -\\frac{\\pi}{2}\\]<br \/>\n\uc774\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<p><span class=\"example\">\uacfc\uc81c.<\/span> \\(x\\rightarrow\\infty\\) \ub610\ub294 \\(x\\rightarrow -\\infty\\)\uc778 \uadf9\ud55c\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc744 \uc9c1\uc811 \ud574\ubcf4\uc790.<\/p>\n<ol class=\"parenthesis\">\n<li>\uc0ac\uce59\uacc4\uc0b0\uacfc \uad00\ub828\ub41c \uadf9\ud55c\uc758 \ub300\uc218\uc801 \uc131\uc9c8\uc744 \uae30\uc220\ud558\uace0, \uc608\ub97c \ub4e4\uc5b4 \uc124\uba85\ud574 \ubcf4\uc790.<\/li>\n<li>\uc218\uc5f4 \ud310\uc815\ubc95\uc744 \uae30\uc220\ud574 \ubcf4\uc790.<\/li>\n<li>\ubd80\ub4f1\uc2dd\uacfc \uad00\ub828\ub41c \uadf9\ud55c\uc758 \uc131\uc9c8\uc744 \uae30\uc220\ud574 \ubcf4\uc790.<\/li>\n<li>\uc870\uc784 \uc815\ub9ac\ub97c \uae30\uc220\ud558\uace0, \uc608\ub97c \ub4e4\uc5b4 \uc124\uba85\ud574 \ubcf4\uc790.<\/li>\n<\/ol>\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\u201c\u201d\n\u2018\u2019\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<p><!--\n\n\n<div style=\"display: none; visibility: hidden;\">\n\\[\n\\newcommand{\\Hom}{{\\operatorname{Hom}}}\n\\newcommand{\\Mat}{{\\operatorname{Mat}}}\n\\newcommand{\\proj}{{\\operatorname{proj}}}\n\\newcommand{\\adj}{{\\operatorname{adj}}}\n\\]\n<\/div>\n\n\n--><\/p>\n<div class=\"box itc_prev_next_box\">\n<ul class=\"itc_ul\">\n<li class=\"itc_li_prev\">\uc55e\uc758 \uae00 : <a href=\"..\/one-sided-limits\">\uc88c\uadf9\ud55c\uacfc \uc6b0\uadf9\ud55c<\/a><\/li>\n<li class=\"itc_li_next\">\ub2e4\uc74c \uae00 : <a href=\"..\/asymptotes\">\ud568\uc218\uc758 \uadf8\ub798\ud504\uc758 \uc810\uadfc\uc120<\/a><\/li>\n<\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 3\uc7a5 4\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; (\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30) \uc9d1\ud569 \\(D\\)\uac00 \uc704\ub85c \uc720\uacc4\uac00 \uc544\ub2c8\ub77c\uace0 \ud558\uace0, \ud568\uc218 \\(f:D \\rightarrow \\mathbb{R}\\)\ub97c \uc0dd\uac01\ud558\uc790. \ub9cc\uc57d \\(x\\)\uac00 \\(D\\)\uc5d0 \uc18d\ud55c \uc0c1\ud0dc\ub85c \ubb34\ud55c\ud788 \ucee4\uc9c8 \ub54c \\(f(x)\\)\uac00 \ud558\ub098\uc758 \uac12 \\(L\\)\uc5d0 \ud55c \uc5c6\uc774 \uac00\uae4c\uc774 \ub2e4\uac00\uac04\ub2e4\uba74 \u201c\\(x\\rightarrow\\infty\\)\uc77c \ub54c \\(f(x)\\)\uac00 \\(L\\)\uc5d0 \uc218\ub834\ud55c\ub2e4\u201d\ub77c\uace0 \ub9d0\ud55c\ub2e4. \uc774\ub54c \\(L\\)\uc744 \uc591\uc758 \ubb34\ud55c\ub300\uc5d0\uc11c \\(\\boldsymbol{f(x)}\\)\uc758 \uadf9\ud55c\uc774\ub77c\uace0 \ubd80\ub974\uba70, \uc774 \uc0ac\uc2e4\uc744 \\(\\lim_{x\\rightarrow\\infty}f(x)=L\\) \ub610\ub294 \\(f(x) \\rightarrow L \\,\\text{as}\\, x\\rightarrow\\infty\\) \uc640 \uac19\uc774 \ub098\ud0c0\ub0b8\ub2e4. \ub9cc\uc57d&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":6620,"menu_order":304,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"class_list":["post-6697","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6697","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=6697"}],"version-history":[{"count":13,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6697\/revisions"}],"predecessor-version":[{"id":7323,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6697\/revisions\/7323"}],"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=6697"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}