{"id":6705,"date":"2021-07-21T00:00:14","date_gmt":"2021-07-20T15:00:14","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=6705"},"modified":"2026-09-27T20:18:55","modified_gmt":"2026-09-27T11:18:55","slug":"theorems-on-continuity","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-calculus\/theorems-on-continuity\/","title":{"rendered":"\uc5f0\uc18d\uc131\uacfc \uad00\ub828\ub41c \uc815\ub9ac"},"content":{"rendered":"<style type=\"text\/css\">\n\timg.mfp-img { background-color: white; }\n<\/style>\n<div class=\"box itc_intro\">\n<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 4\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>\uc774 \uc808\uc5d0\uc11c\ub294 \uc5f0\uc18d\uc131\uacfc \uad00\ub828\ub41c \uc815\ub9ac \ub124 \uac1c\ub97c \uc0b4\ud3b4\ubcf8\ub2e4.<\/p>\n<p>\uc774 \uae00\uc5d0\uc11c\ub294 \uc9c1\uad00\uc801\uc778 \uc99d\uba85\uc744 \uc18c\uac1c\ud55c\ub2e4. \uc5c4\ubc00\ud55c \uc99d\uba85\uc744 \ubcf4\uace0\uc790 \ud55c\ub2e4\uba74 \ub2e4\uc74c \uac8c\uc2dc\uae00\uc744 \ud655\uc778\ud558\uae30 \ubc14\ub780\ub2e4: <a href=\"https:\/\/sasamath.com\/blog\/articles\/calculus-continuity\">\uc5f0\uc18d\ud568\uc218<\/a>.<\/p>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\uc5f0\uc18d\ud568\uc218\uc758 \uc0ac\uc787\uac12 \uc815\ub9ac<\/h2>\n<p>\\([a,\\,b]\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \uad6c\uac04\uc774\uace0 \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc5f0\uc18d\uc778 \uc2e4\uc22b\uac12 \ud568\uc218\ub77c\uace0 \ud558\uc790. \ub610\ud55c \\(f(a) < f(b)\\)\ub77c\uace0 \ud558\uc790. \\(C\\)\uac00 \\(f(a) < C < f(b)\\)\uc778 \uc2e4\uc218\ub77c\uace0 \ud558\uc790. \uc9d1\ud569\n\\[\nE=\\left\\{x\\in[a,\\,b]\\,\\vert\\,f(x)\\le C\\right\\}\n\\]\n\ub97c \uc0dd\uac01\ud558\uc790. \\(E\\)\ub294 \uacf5\uc9d1\ud569\uc774 \uc544\ub2c8\uace0 \uc704\ub85c \uc720\uacc4\uc774\ubbc0\ub85c \ucd5c\uc18c\uc0c1\uacc4 \\(c=\\sup E\\)\ub97c \uac00\uc9c4\ub2e4.<\/p>\n<p>\\(f(a) < C\\)\uc774\uace0 \\(f\\)\uac00 \\(a\\)\uc5d0\uc11c \uc6b0\uc5f0\uc18d\uc774\ubbc0\ub85c \\(E\\)\uc5d0\ub294 \\(a\\)\ubcf4\ub2e4 \ud070 \uc810\uc774 \uc874\uc7ac\ud55c\ub2e4. \ub610\ud55c \\(f(b)>C\\)\uc774\uace0 \\(f\\)\uac00 \\(b\\)\uc5d0\uc11c \uc88c\uc5f0\uc18d\uc774\ubbc0\ub85c \\(b\\)\uc5d0 \ucda9\ubd84\ud788 \uac00\uae4c\uc6b4 \uc810\ub4e4\uc740 \\(E\\)\uc5d0 \uc18d\ud558\uc9c0 \uc54a\ub294\ub2e4. \ub530\ub77c\uc11c<br \/>\n\\[<br \/>\na < c < b\n\\]\n\uc774\ub2e4.<\/p>\n<p>\ub9cc\uc57d \\(f(c) < C\\)\ub77c\uba74 \\(f\\)\uc758 \uc5f0\uc18d\uc131\uc5d0 \uc758\ud558\uc5ec \\(c\\)\ubcf4\ub2e4 \uc870\uae08 \ud070 \uc810 \\(x\\)\uc5d0 \ub300\ud574\uc11c\ub3c4 \\(f(x) < C\\)\uac00 \uc131\ub9bd\ud55c\ub2e4. \uadf8\ub7ec\uba74 \\(x\\in E\\)\uc774\uba74\uc11c \\(x>c\\)\uac00 \ub418\uc5b4 \\(c\\)\uac00 \\(E\\)\uc758 \uc0c1\uacc4\ub77c\ub294 \uc0ac\uc2e4\uc5d0 \ubaa8\uc21c\uc774\ub2e4.<\/p>\n<p>\ubc18\ub300\ub85c \\(f(c)>C\\)\ub77c\uba74 \\(f\\)\uc758 \uc5f0\uc18d\uc131\uc5d0 \uc758\ud558\uc5ec \\(c\\)\uc5d0 \ucda9\ubd84\ud788 \uac00\uae4c\uc6b4 \uc810\uc5d0\uc11c\ub294 \\(f(x)>C\\)\uc774\ub2e4. \uadf8\ub7ec\uba74 \\(c\\)\ubcf4\ub2e4 \uc791\uc740 \uc5b4\ub5a4 \uc218\uac00 \\(E\\)\uc758 \uc0c1\uacc4\uac00 \ub418\uc5b4 \\(c\\)\uac00 \\(E\\)\uc758 \ucd5c\uc18c\uc0c1\uacc4\ub77c\ub294 \uc0ac\uc2e4\uc5d0 \ubaa8\uc21c\uc774\ub2e4.<\/p>\n<p>\ub530\ub77c\uc11c<br \/>\n\\[<br \/>\nf(c)=C<br \/>\n\\]<br \/>\n\uc774\ub2e4.<\/p>\n<p>\uc774\uc640 \uac19\uc740 \uc0c1\ud669\uc740 \ub2e4\uc74c \uadf8\ub9bc\uc73c\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4.<\/p>\n<div>\n<a href=\"\/blog\/wp-content\/uploads\/2021\/09\/ic_403_1.png\" data-rel=\"penci-gallery-image-content\" ><img fetchpriority=\"high\" decoding=\"async\" src=\"\/blog\/wp-content\/uploads\/2021\/09\/ic_403_1.png\" alt=\"\" width=\"325\" height=\"159\" class=\"aligncenter size-full wp-image-7785\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_1.png 1950w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_1-300x147.png 300w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_1-1024x501.png 1024w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_1-768x376.png 768w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_1-1536x751.png 1536w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_1-1920x939.png 1920w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_1-1170x572.png 1170w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_1-585x286.png 585w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><\/a>\n<\/div>\n<p>\uc774\ub85c\uc368 \ub2e4\uc74c \uc815\ub9ac\ub97c \uc5bb\ub294\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 4.3.1. (\uc5f0\uc18d\ud568\uc218\uc758 \uc0ac\uc787\uac12 \uc815\ub9ac)<\/span><\/p>\n<p>\\([a,\\,b]\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \uad6c\uac04\uc774\uace0 \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc5f0\uc18d\uc778 \uc2e4\uc22b\uac12 \ud568\uc218\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(f\\)\ub294 \\([a,\\,b]\\)\uc5d0\uc11c \\(f(a)\\)\uc640 \\(f(b)\\) \uc0ac\uc774\uc5d0 \uc788\ub294 \ubaa8\ub4e0 \uac12\uc744 \ucde8\ud55c\ub2e4. \uc989 \ub9cc\uc57d \\(f(a) \\ne f(b)\\)\uc774\uace0 \\(C\\)\uac00 \\(f(a)\\)\uc640 \\(f(b)\\) \uc0ac\uc774\uc5d0 \uc788\ub294 \uac12\uc774\uba74, \\(f(c)=C\\)\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc810 \\(c\\)\uac00 \uad6c\uac04 \\((a,\\,b)\\)\uc5d0 \uc874\uc7ac\ud55c\ub2e4.\n<\/p>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\uc608\uc81c 4.3.1.<\/span><br \/>\n\ubc29\uc815\uc2dd \\(x^5 &#8211; x^2 &#8211; 1 = 0\\)\uc774 \uc5f4\ub9b0\uad6c\uac04 \\((0,\\,2)\\)\uc5d0\uc11c \uc801\uc5b4\ub3c4 \ud558\ub098\uc758 \uadfc\uc744 \uac00\uc9d0\uc744 \ubcf4\uc774\uc2dc\uc624.<\/p>\n<p class=\"margintop1\"><span class=\"proof\">\ud480\uc774.<\/span><br \/>\n\\(f(x) = x^5 &#8211; x^2 &#8211; 1\\)\uc774\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(f\\)\ub294 \\(\\mathbb{R}\\)\uc5d0\uc11c \uc5f0\uc18d\uc778 \ud568\uc218\uc774\ub2e4. \\(f(0) = -1\\)\uc774\uace0 \\(f(2) = 27\\)\uc774\ubbc0\ub85c \uc0ac\uc787\uac12 \uc815\ub9ac\uc5d0 \uc758\ud558\uc5ec \\(f(c)=0\\)\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc810 \\(c\\)\uac00 \uc5f4\ub9b0\uad6c\uac04 \\((0,\\,2)\\)\uc5d0 \uc874\uc7ac\ud55c\ub2e4. \uadf8\ub7ec\ud55c \uc810 \\(c\\)\uac00 \ubc14\ub85c \ubc29\uc815\uc2dd\uc758 \uadfc\uc774\ub2e4.\n<\/p>\n<\/div>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\uc5f0\uc18d\ud568\uc218\uc758 \ucd5c\ub300 \ucd5c\uc18c \uc815\ub9ac<\/h2>\n<p>\\([a,\\,b]\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \uad6c\uac04\uc774\uace0 \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc5f0\uc18d\uc778 \uc2e4\uc22b\uac12 \ud568\uc218\ub77c\uace0 \ud558\uc790. \uc774\uc81c \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc720\uacc4\uc784\uc744 \ubcf4\uc77c \uac83\uc774\ub2e4.<\/p>\n<p>\uacb0\ub860\uacfc\ub294 \ubc18\ub300\ub85c \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc720\uacc4\uac00 \uc544\ub2c8\ub77c\uace0 \uac00\uc815\ud558\uc790. \uadf8\ub7ec\uba74 \\(f\\)\ub294 \\([a,\\,b]\\)\uc5d0\uc11c \uc704\ub85c \uc720\uacc4\uac00 \uc544\ub2c8\uac70\ub098 \uc544\ub798\ub85c \uc720\uacc4\uac00 \uc544\ub2c8\ub2e4. \uc77c\ubc18\uc131\uc744 \uc783\uc9c0 \uc54a\uace0 \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc704\ub85c \uc720\uacc4\uac00 \uc544\ub2c8\ub77c\uace0 \uac00\uc815\ud558\uc790.<\/p>\n<p>\\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc704\ub85c \uc720\uacc4\uac00 \uc544\ub2c8\ubbc0\ub85c, \\(n\\)\uc774 \uc591\uc758 \uc815\uc218\uc77c \ub54c \\(f(x_n ) > n\\)\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc810 \\(x_n\\)\uc774 \\([a,\\,b]\\)\uc5d0 \uc874\uc7ac\ud55c\ub2e4. \uc774\uc640 \uac19\uc774 \uc5bb\uc5b4\uc9c4 \uc218\uc5f4 \\(\\left\\{ x_n \\right\\}\\)\uc774 \uc720\uacc4\uc778 \uc218\uc5f4\uc774\ubbc0\ub85c, \ubcfc\ucc28\ub178-\ubc14\uc774\uc5b4\uc288\ud2b8\ub77c\uc2a4 \uc815\ub9ac\uc5d0 \uc758\ud558\uc5ec \uc218\ub834\ud558\ub294 \ubd80\ubd84\uc218\uc5f4 \\(\\left\\{ x_{n_k}\\right\\}\\)\uac00 \uc874\uc7ac\ud55c\ub2e4. \\(\\left\\{ x_{n_k}\\right\\}\\)\uac00 \\(c\\)\uc5d0 \uc218\ub834\ud55c\ub2e4\uace0 \ud558\uc790. \\(\\left\\{ x_{n_k}\\right\\}\\)\uc758 \ubaa8\ub4e0 \ud56d\uc774 \\([a,\\,b]\\)\uc5d0 \uc18d\ud558\ubbc0\ub85c \\(c\\) \ub610\ud55c \\([a,\\,b]\\)\uc5d0 \uc18d\ud55c\ub2e4.<\/p>\n<p>\\(f\\)\uac00 \\(c\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\ubbc0\ub85c \uc218\uc5f4 \uc5f0\uc18d\uc5d0 \uc758\ud558\uc5ec<br \/>\n\\[<br \/>\n\\lim_{k\\rightarrow\\infty} f(x_{n_k})=f(c)<br \/>\n\\]<br \/>\n\uc774\ub2e4. \ud55c\ud3b8<br \/>\n\\[<br \/>\nf(x_{n_k})>n_k<br \/>\n\\]<br \/>\n\uc774\uace0 \\(n_k\\rightarrow\\infty\\)\uc774\ubbc0\ub85c \\(f(x_{n_k})\\rightarrow\\infty\\)\uc774\ub2e4. \uc774\uac83\uc740 \ubaa8\uc21c\uc774\ubbc0\ub85c \\(f\\)\ub294 \\([a,\\,b]\\)\uc5d0\uc11c \uc704\ub85c \uc720\uacc4\uc774\ub2e4.<\/p>\n<p>\uac19\uc740 \ubc29\ubc95\uc73c\ub85c \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc544\ub798\ub85c \uc720\uacc4\ub77c\ub294 \uc0ac\uc2e4\ub3c4 \uc99d\uba85\ub41c\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 4.3.2. (\uc5f0\uc18d\ud568\uc218\uc758 \uc720\uacc4\uc131)<\/span><\/p>\n<p>\\([a,\\,b]\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \uad6c\uac04\uc774\uace0 \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc5f0\uc18d\uc778 \uc2e4\uc22b\uac12 \ud568\uc218\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc720\uacc4\uc774\ub2e4.\n<\/p>\n<\/div>\n<p>\uac19\uc740 \uc870\uac74 \uc544\ub798\uc5d0\uc11c \ub354 \ud765\ubbf8\ub85c\uc6b4 \uacb0\uacfc\ub97c \ub04c\uc5b4\ub0bc \uc218 \uc788\ub2e4.<\/p>\n<p class=\"aligncenter\">\u201c\ubaa8\ub4e0 \\(x\\in [a,\\,b]\\)\uc5d0 \ub300\ud558\uc5ec \\(f(x) \\le M\\)\u201d<\/p>\n<p>\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc2e4\uc218 \\(M\\) \uc911\uc5d0\uc11c \uac00\uc7a5 \uc791\uc740 \uac12\uc744 \ud0dd\ud558\uc790. \uadf8\ub7ec\uba74 \\(n\\)\uc774 \uc591\uc758 \uc815\uc218\uc77c \ub54c<br \/>\n\\[<br \/>\nf(x_n ) > M &#8211; \\frac{1}{n}<br \/>\n\\]<br \/>\n\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc810 \\(x_n\\)\uc774 \\([a,\\,b]\\)\uc5d0 \uc874\uc7ac\ud55c\ub2e4.<\/p>\n<div>\n<a href=\"\/blog\/wp-content\/uploads\/2021\/09\/ic_403_2.png\" data-rel=\"penci-gallery-image-content\" ><img decoding=\"async\" src=\"\/blog\/wp-content\/uploads\/2021\/09\/ic_403_2.png\" alt=\"\" width=\"368\" height=\"169\" class=\"aligncenter size-full wp-image-7786\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_2.png 2208w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_2-300x138.png 300w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_2-1024x469.png 1024w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_2-768x352.png 768w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_2-1536x704.png 1536w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_2-2048x939.png 2048w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_2-1920x880.png 1920w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_2-1170x536.png 1170w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_2-585x268.png 585w\" sizes=\"(max-width: 368px) 100vw, 368px\" \/><\/a>\n<\/div>\n<p>\\(\\left\\{ x_n \\right\\}\\)\uc774 \uc720\uacc4\uc778 \uc218\uc5f4\uc774\ubbc0\ub85c \ubcfc\ucc28\ub178-\ubc14\uc774\uc5b4\uc288\ud2b8\ub77c\uc2a4 \uc815\ub9ac\uc5d0 \uc758\ud558\uc5ec \uc218\ub834\ud558\ub294 \ubd80\ubd84\uc218\uc5f4 \\(\\left\\{ x_{n_k}\\right\\}\\)\uac00 \uc874\uc7ac\ud55c\ub2e4. \\(\\left\\{ x_{n_k}\\right\\}\\)\uac00 \\(c\\)\uc5d0 \uc218\ub834\ud55c\ub2e4\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(c\\in [a,\\,b]\\)\uc774\ub2e4. \uadf8\ub7f0\ub370<br \/>\n\\[<br \/>\nM \\ge f(x_{n_k}) > M &#8211; \\frac{1}{n_k}<br \/>\n\\]<br \/>\n\uc774\ubbc0\ub85c<br \/>\n\\[<br \/>\n\\lim_{k\\rightarrow\\infty} f(x_{n_k}) = M<br \/>\n\\]<br \/>\n\uc774 \uc131\ub9bd\ud55c\ub2e4. \ub354\uc6b1\uc774 \\(f\\)\uac00 \\(c\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\ubbc0\ub85c \uc218\uc5f4 \uc5f0\uc18d\uc5d0 \uc758\ud558\uc5ec<br \/>\n\\[<br \/>\n\\lim_{k\\rightarrow\\infty} f(x_{n_k}) = f(c)<br \/>\n\\]<br \/>\n\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c<br \/>\n\\[<br \/>\nf(c)=M<br \/>\n\\]<br \/>\n\uc774\uace0, \\(f\\)\ub294 \\([a,\\,b]\\)\uc758 \uc810 \\(c\\)\uc5d0\uc11c \ucd5c\ub313\uac12\uc744 \uac00\uc9c4\ub2e4.<\/p>\n<p>\uac19\uc740 \ubc29\ubc95\uc73c\ub85c \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \ucd5c\uc19f\uac12\uc744 \uac00\uc9c4\ub2e4\ub294 \uc0ac\uc2e4\ub3c4 \uc99d\uba85\ub41c\ub2e4.<\/p>\n<p>\uc774\ub85c\uc368 \ub2e4\uc74c \uc815\ub9ac\ub97c \uc99d\uba85\ud558\uc600\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 4.3.3. (\uc5f0\uc18d\ud568\uc218\uc758 \ucd5c\ub300 \ucd5c\uc18c \uc815\ub9ac)<\/span><\/p>\n<p>\\([a,\\,b]\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \uad6c\uac04\uc774\uace0 \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc5f0\uc18d\uc778 \uc2e4\uc22b\uac12 \ud568\uc218\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \ucd5c\ub313\uac12\uacfc \ucd5c\uc19f\uac12\uc744 \uac00\uc9c4\ub2e4.\n<\/p>\n<\/div>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\uc5ed\ud568\uc218\uc758 \uc5f0\uc18d\uc131<\/h2>\n<p>\uc5f0\uc18d\uc774\uace0 \uc77c\ub300\uc77c\uc778 \ud568\uc218\uc758 \uc5ed\ud568\uc218\uac00 \uc5f0\uc18d\ud568\uc218\uc784\uc744 \uc99d\uba85\ud574 \ubcf4\uc790. \ubbf8\uc801\ubd84\ud559\uc744 \ucc98\uc74c \uacf5\ubd80\ud558\ub294 \uc0ac\ub78c\uc774\ub77c\uba74 \uc774 \uc99d\uba85\uc744 \uc0dd\ub7b5\ud558\uace0 \uc815\ub9ac\uc758 \ub0b4\uc6a9\ub9cc \ud655\uc778\ud574\ub3c4 \uc88b\ub2e4.<\/p>\n<p>\\([a,\\,b]\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \uad6c\uac04\uc774\uace0 \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc5f0\uc18d\uc778 \uc2e4\uc22b\uac12 \ud568\uc218\ub77c\uace0 \ud558\uc790. \ub610\ud55c \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc21c\uc99d\uac00\ud55c\ub2e4\uace0 \ud558\uc790. \uc989<\/p>\n<p class=\"aligncenter\">\\(x_1 < x_2 \\)\uc77c \ub54c \\(f(x_1 ) < f(x_2 )\\)<\/p>\n<p>\uac00 \uc131\ub9bd\ud55c\ub2e4\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(f\\)\ub294 \\([a,\\,b]\\)\uc5d0\uc11c \uc77c\ub300\uc77c\uc778 \ud568\uc218\uc774\ub2e4. \\(A = f(a),\\) \\(B = f(b)\\)\ub77c\uace0 \ud558\uc790. \uc0ac\uc787\uac12 \uc815\ub9ac\uc5d0 \uc758\ud558\uc5ec \\(A\\)\uc640 \\(B\\) \uc0ac\uc774\uc758 \ubaa8\ub4e0 \uac12\uc740 \\(f\\)\uc758 \ud568\uc22b\uac12\uc73c\ub85c \ub098\ud0c0\ub09c\ub2e4. \ub530\ub77c\uc11c \\(f\\)\ub294 \\([a,\\,b]\\)\uc5d0\uc11c \\([A,\\,B]\\)\ub85c\uc758 \uc77c\ub300\uc77c \ub300\uc751\uc774\uba70, \uc5ed\ud568\uc218 \\(g=f^{-1}\\)\uac00 \uc874\uc7ac\ud55c\ub2e4.<\/p>\n<p>\uc774\uc81c \\(g\\)\uac00 \\([A,\\,B]\\)\uc5d0\uc11c \uc5f0\uc18d\uc784\uc744 \ubcf4\uc774\uc790. \\(C\\in [A,\\,B]\\)\ub77c\uace0 \ud558\uc790. \uba3c\uc800 \\(A < C < B\\)\uc778 \uacbd\uc6b0\ub97c \uc0dd\uac01\ud558\uc790. \\(g(C)=c\\)\ub77c\uace0 \ud558\uc790. \\(g\\)\uac00 \uc99d\uac00\ud568\uc218\uc774\ubbc0\ub85c \ub2e8\uc870\uc218\ub834 \uc815\ub9ac\uc5d0 \uc758\ud558\uc5ec \\(C\\)\uc5d0\uc11c \\(g\\)\uc758 \uc88c\uadf9\ud55c\uacfc \uc6b0\uadf9\ud55c\uc774 \uc218\ub834\ud55c\ub2e4. \\(C\\)\uc5d0\uc11c \\(g\\)\uc758 \uc88c\uadf9\ud55c\uc744 \\(p,\\) \uc6b0\uadf9\ud55c\uc744 \\(q\\)\ub77c\uace0 \ud558\uc790. \uc989\n\\[\n\\lim_{y\\rightarrow C^-} g(y) = p ,\\quad \\, \\lim_{y\\rightarrow C^+} g(y) = q\n\\]\n\ub77c\uace0 \ud558\uc790. \\(g(C) = c\\)\uc774\uace0 \\(g\\)\uac00 \uc21c\uc99d\uac00\ud558\ubbc0\ub85c\n\\[\np\\le c\\le q\n\\]\n\uc774\ub2e4.<\/p>\n<div>\n<a href=\"\/blog\/wp-content\/uploads\/2021\/09\/ic_403_34.png\" data-rel=\"penci-gallery-image-content\" ><img decoding=\"async\" src=\"\/blog\/wp-content\/uploads\/2021\/09\/ic_403_34.png\" alt=\"\" width=\"536\" height=\"230\" class=\"aligncenter size-full wp-image-7789\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_34.png 3213w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_34-300x129.png 300w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_34-1024x439.png 1024w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_34-768x330.png 768w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_34-1536x659.png 1536w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_34-2048x879.png 2048w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_34-1920x824.png 1920w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_34-1170x502.png 1170w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_403_34-585x251.png 585w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/a>\n<\/div>\n<p>\\(p < c\\)\ub77c\uace0 \uac00\uc815\ud558\uace0, \\(p\\)\uc640 \\(c\\) \uc0ac\uc774\uc5d0 \uc788\ub294 \uac12 \\(x_1\\)\uc744 \ud0dd\ud558\uc790. \uadf8\ub7ec\uba74\n\\[\np < x_1 < c\n\\]\n\uc774\uace0 \\(f\\)\uac00 \uc21c\uc99d\uac00\ud558\ubbc0\ub85c\n\\[\nf(x_1) < f(c)=C\n\\]\n\uc774\ub2e4. \ud55c\ud3b8\n\\[\n\\lim_{y\\rightarrow C^-}g(y)=p < x_1\n\\]\n\uc774\ubbc0\ub85c \\(C\\)\ubcf4\ub2e4 \uc791\uace0 \\(C\\)\uc5d0 \ucda9\ubd84\ud788 \uac00\uae4c\uc6b4 \\(y\\)\uc5d0 \ub300\ud558\uc5ec\n\\[\ng(y) < x_1\n\\]\n\uc774\ub2e4. \uc774\ub7ec\ud55c \\(y\\)\ub97c\n\\[\nf(x_1) < y < C\n\\]\n\uac00 \ub418\ub3c4\ub85d \ud0dd\ud560 \uc218 \uc788\ub2e4. \uadf8\ub7f0\ub370 \\(f\\)\uac00 \uc21c\uc99d\uac00\ud558\ubbc0\ub85c\n\\[\ny=f(g(y)) < f(x_1)\n\\]\n\uc774\uc5b4\uc57c \ud55c\ub2e4. \uc774\uac83\uc740 \\(f(x_1) < y\\)\uc640 \ubaa8\uc21c\uc774\ub2e4. \ub530\ub77c\uc11c\n\\[\np=c\n\\]\n\uc774\ub2e4.<\/p>\n<p>\ub9c8\ucc2c\uac00\uc9c0\ub85c \\(c < q\\)\ub77c\uace0 \uac00\uc815\ud558\uace0 \\(c < x_2 < q\\)\uc778 \\(x_2\\)\ub97c \ud0dd\ud558\uba74 \ubaa8\uc21c\uc744 \uc5bb\ub294\ub2e4. \ub530\ub77c\uc11c\n\\[\nq=c\n\\]\n\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c\n\\[\n\\lim_{y\\rightarrow C^-} g(y)\n=\n\\lim_{y\\rightarrow C^+} g(y)\n=\nc\n=\ng(C)\n\\]\n\uc774\ub2e4. \ub530\ub77c\uc11c \\(g\\)\uac00 \\(C\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\ub2e4.<\/p>\n<p>\ub05d\uc810 \\(A\\)\uc640 \\(B\\)\uc5d0\uc11c\ub3c4 \uac19\uc740 \ub17c\ubc95\uc73c\ub85c \uac01\uac01<br \/>\n\\[<br \/>\n\\lim_{y\\rightarrow A^+}g(y)=g(A),<br \/>\n\\qquad<br \/>\n\\lim_{y\\rightarrow B^-}g(y)=g(B)<br \/>\n\\]<br \/>\n\ub97c \uc5bb\ub294\ub2e4. \ub530\ub77c\uc11c \\(g\\)\ub294 \\([A,\\,B]\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\ub2e4.<\/p>\n<p>\\(f\\)\uac00 \uc21c\uac10\uc18c\ud558\ub294 \uacbd\uc6b0\ub3c4 \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \uc99d\uba85\ud560 \uc218 \uc788\ub2e4. \ub610\ud55c \ub2eb\ud78c\uad6c\uac04\uc5d0\uc11c \uc5f0\uc18d\uc774\uace0 \uc77c\ub300\uc77c\uc778 \ud568\uc218\ub294 \uc21c\uc99d\uac00\ud558\uac70\ub098 \uc21c\uac10\uc18c\ud55c\ub2e4. \uc774 \uc0ac\uc2e4\uc740 \uc0ac\uc787\uac12 \uc815\ub9ac\ub97c \uc774\uc6a9\ud558\uc5ec \uc99d\uba85\ud560 \uc218 \uc788\ub2e4.<\/p>\n<p>\uc774\ub85c\uc368 \ub2e4\uc74c \uc815\ub9ac\ub97c \uc5bb\ub294\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 4.3.4. (\uc5ed\ud568\uc218\uc758 \uc5f0\uc18d\uc131)<\/span><\/p>\n<p>\\([a,\\,b]\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \uad6c\uac04\uc774\uace0 \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc5f0\uc18d\uc778 \uc2e4\uc22b\uac12 \ud568\uc218\uc774\uba70 \uc77c\ub300\uc77c\uc774\ub77c\uace0 \ud558\uc790. \ub610\ud55c \\([a,\\,b]\\)\uc5d0\uc11c \\(f\\)\uc758 \uc0c1(image)\uc744 \\(I\\)\ub77c\uace0 \ud558\uc790. \ub9cc\uc57d \\(g\\)\uac00 \\(f\\)\uc758 \uc5ed\ud568\uc218\uc774\uba74 \\(g\\)\ub294 \\(I\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\ub2e4.\n<\/p>\n<\/div>\n<p>\uc704\uc5d0\uc11c \uc0ac\uc6a9\ud55c \u201c\ub2eb\ud78c\uad6c\uac04\uc5d0\uc11c \uc5f0\uc18d\uc774\uace0 \uc77c\ub300\uc77c\uc778 \ud568\uc218\ub294 \uc21c\uc99d\uac00\ud558\uac70\ub098 \uc21c\uac10\uc18c\ud55c\ub2e4\u201d\ub77c\ub294 \uc0ac\uc2e4\uc740 \uc5b4\ub835\uc9c0 \uc54a\uc73c\ub2c8 \uc9c1\uc811 \uc99d\uba85\ud574 \ubcf4\uae30 \ubc14\ub780\ub2e4. (\uc0ac\uc787\uac12 \uc815\ub9ac\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc99d\uba85\ud560 \uc218 \uc788\ub2e4.)<\/p>\n<div class=\"example\">\n<p><span class=\"example\">\ubcf4\uae30 4.3.2.<\/span><br \/>\n\\(x\\ge0\\)\uc778 \ubc94\uc704\uc5d0\uc11c \\(f(x) = \\sqrt{x}\\)\ub77c\uace0 \ud558\uc790. \uc784\uc758\uc758 \uc591\uc218 \\(M\\)\uc5d0 \ub300\ud558\uc5ec \ud568\uc218 \\(g(x)=x^2\\)\uc740 \uad6c\uac04 \\([0,\\,M]\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\uace0 \uc21c\uc99d\uac00\ud558\uba70, \uadf8 \uc5ed\ud568\uc218\ub294 \\(f(x)=\\sqrt{x}\\)\uc774\ub2e4. \ub530\ub77c\uc11c \uc815\ub9ac 4.3.4\uc5d0 \uc758\ud558\uc5ec \\(f\\)\ub294 \\([0,\\,M^2]\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\ub2e4. \\(M\\)\uc744 \uc784\uc758\ub85c \ud0dd\ud560 \uc218 \uc788\uc73c\ubbc0\ub85c \\(f\\)\ub294 \\([0,\\,\\infty)\\)\uc5d0\uc11c \uc5f0\uc18d\ud568\uc218\uc774\ub2e4.\n<\/p>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\ubcf4\uae30 4.3.3.<\/span><br \/>\n\\(f(x) = \\sin x\\)\ub77c\uace0 \ud558\uc790. \\(f\\)\uac00 \ub2eb\ud78c\uad6c\uac04<br \/>\n\\[<br \/>\nI = \\left[ &#8211; \\frac{\\pi}{2} ,\\, \\frac{\\pi}{2}\\right]<br \/>\n\\]<br \/>\n\uc5d0\uc11c \uc5f0\uc18d\uc774\uace0 \uc21c\uc99d\uac00\ud558\ubbc0\ub85c, \uadf8 \uc5ed\ud568\uc218<br \/>\n\\[<br \/>\ng(x) = \\sin^{-1} x<br \/>\n\\]<br \/>\n\ub294 \uad6c\uac04 \\([-1 ,\\,1]\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\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\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=\"..\/properties-of-continuous-functions\">\uc5f0\uc18d\ud568\uc218\uc758 \uc131\uc9c8<\/a><\/li>\n<li class=\"itc_li_next\">\ub2e4\uc74c \uae00 : <a href=\"..\/functions-of-several-variables\">\ub2e4\ubcc0\uc218\ud568\uc218\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 4\uc7a5 3\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; (\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30) \uc774 \uc808\uc5d0\uc11c\ub294 \uc5f0\uc18d\uc131\uacfc \uad00\ub828\ub41c \uc815\ub9ac \ub124 \uac1c\ub97c \uc0b4\ud3b4\ubcf8\ub2e4. \uc774 \uae00\uc5d0\uc11c\ub294 \uc9c1\uad00\uc801\uc778 \uc99d\uba85\uc744 \uc18c\uac1c\ud55c\ub2e4. \uc5c4\ubc00\ud55c \uc99d\uba85\uc744 \ubcf4\uace0\uc790 \ud55c\ub2e4\uba74 \ub2e4\uc74c \uac8c\uc2dc\uae00\uc744 \ud655\uc778\ud558\uae30 \ubc14\ub780\ub2e4: \uc5f0\uc18d\ud568\uc218. \uc5f0\uc18d\ud568\uc218\uc758 \uc0ac\uc787\uac12 \uc815\ub9ac \\([a,\\,b]\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \uad6c\uac04\uc774\uace0 \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc5f0\uc18d\uc778 \uc2e4\uc22b\uac12 \ud568\uc218\ub77c\uace0 \ud558\uc790. \ub610\ud55c \\(f(a) < f(b)\\)\ub77c\uace0 \ud558\uc790. \\(C\\)\uac00 \\(f(a) < C < f(b)\\)\uc778 \uc2e4\uc218\ub77c\uace0 \ud558\uc790. \uc9d1\ud569 \\( E=\\left\\{x\\in[a,\\,b]\\,\\vert\\,f(x)\\le C\\right\\} \\)&hellip;\n<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":6620,"menu_order":403,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"class_list":["post-6705","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6705","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=6705"}],"version-history":[{"count":23,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6705\/revisions"}],"predecessor-version":[{"id":10150,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6705\/revisions\/10150"}],"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=6705"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}