{"id":23,"date":"2023-09-17T11:07:18","date_gmt":"2023-09-17T11:07:18","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e4%b8%8d%e9%80%a3%e7%b6%9a%e6%80%a7%e3%81%ae%e7%a8%ae%e9%a1%9e\/"},"modified":"2023-09-17T11:07:18","modified_gmt":"2023-09-17T11:07:18","slug":"%e4%b8%8d%e9%80%a3%e7%b6%9a%e6%80%a7%e3%81%ae%e7%a8%ae%e9%a1%9e","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e4%b8%8d%e9%80%a3%e7%b6%9a%e6%80%a7%e3%81%ae%e7%a8%ae%e9%a1%9e\/","title":{"rendered":"\u4e0d\u9023\u7d9a\u6027\u306e\u7a2e\u985e"},"content":{"rendered":"<p>\u3053\u3053\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306a\u7a2e\u985e\u306e\u4e0d\u9023\u7d9a\u6027\u304c\u5b58\u5728\u3059\u308b\u304b\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u3042\u3089\u3086\u308b\u7a2e\u985e\u306e\u4e0d\u9023\u7d9a\u6027\u306e\u4f8b\u3092\u78ba\u8a8d\u3067\u304d\u3001\u95a2\u6570\u306e\u4e0d\u9023\u7d9a\u6027\u306e\u7a2e\u985e\u306b\u95a2\u3059\u308b\u89e3\u7b54\u6e08\u307f\u306e\u6f14\u7fd2\u3092\u4f7f\u7528\u3057\u3066\u7df4\u7fd2\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>\n<p><strong><\/strong><\/p>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><strong> <\/strong><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcuales-son-todos-los-tipos-de-discontinuidades\"><\/span>\u3042\u3089\u3086\u308b\u7a2e\u985e\u306e\u4e0d\u9023\u7d9a\u6027\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e0d\u9023\u7d9a\u6027\u306b\u306f\u6b21\u306e 3 \u3064\u306e\u30bf\u30a4\u30d7\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li><strong>\u56de\u907f\u53ef\u80fd\u306a\u4e0d\u9023\u7d9a\u6027<\/strong>: \u3042\u308b\u70b9\u306b\u304a\u3051\u308b\u95a2\u6570\u306e\u6a2a\u65b9\u5411\u306e\u9650\u754c\u304c\u95a2\u6570\u306e\u5024\u3068\u4e00\u81f4\u3057\u307e\u305b\u3093\u3002<\/li>\n<li><strong>\u907f\u3051\u3089\u308c\u306a\u3044\u6709\u9650\u30b8\u30e3\u30f3\u30d7\u306e\u4e0d\u9023\u7d9a\u6027<\/strong>: \u3042\u308b\u70b9\u306b\u304a\u3051\u308b\u95a2\u6570\u306e\u6a2a\u65b9\u5411\u306e\u9650\u754c\u304c\u7570\u306a\u308a\u307e\u3059\u3002<\/li>\n<li><strong>\u907f\u3051\u3089\u308c\u306a\u3044\u7121\u9650\u30b8\u30e3\u30f3\u30d7\u306e\u4e0d\u9023\u7d9a\u6027<\/strong>: \u95a2\u6570\u306e\u6a2a\u65b9\u5411\u306e\u5236\u9650\u306e 1 \u3064\u304c\u7121\u9650\u5927\u3092\u4e0e\u3048\u308b\u304b\u3001\u5b58\u5728\u3057\u307e\u305b\u3093\u3002<\/li>\n<\/ul>\n<p>\u6982\u5ff5\u306e\u7406\u89e3\u3092\u7d42\u3048\u308b\u305f\u3081\u306b\u3001\u5404\u30bf\u30a4\u30d7\u306e\u4e0d\u9023\u7d9a\u6027\u3092\u3088\u308a\u8a73\u7d30\u306b\u8aac\u660e\u3057\u30013 \u3064\u306e\u30bf\u30a4\u30d7\u306e\u4e0d\u9023\u7d9a\u6027\u3092\u4f7f\u7528\u3057\u305f\u95a2\u6570\u306e\u4f8b\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"discontinuidad-evitable\"><\/span> \u56de\u907f\u53ef\u80fd\u306a\u4e0d\u9023\u7d9a\u6027<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><strong> <\/strong><\/div>\n<\/div>\n<p><strong>\u56de\u907f\u53ef\u80fd\u306a\u4e0d\u9023\u7d9a\u6027\u306f<\/strong>\u3001\u305d\u306e\u70b9\u306b\u5883\u754c\u304c\u5b58\u5728\u3059\u308b\u304c\u3001\u95a2\u6570\u306e\u5024\u3068\u4e00\u81f4\u3057\u306a\u3044\u5834\u5408\u3001\u307e\u305f\u306f\u95a2\u6570\u306e\u30a4\u30e1\u30fc\u30b8\u304c\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u306b\u3001\u305d\u306e\u70b9\u306b\u95a2\u6570\u304c\u3042\u308b\u4e0d\u9023\u7d9a\u6027\u306e\u4e00\u7a2e\u3067\u3059\u3002 <\/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-c26b9be97568ba85e1f8f22b568a2354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\exists \\lim_{x \\to a} f(x) \\neq f(a) \\qquad | \\qquad \\displaystyle \\exists\\lim_{x \\to a} f(x) \\text{ y } \\ \\cancel{\\exists} \\ f(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"367\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-columns are-vertically-aligned-top is-layout-flex wp-container-99\">\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow\">\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/discontinuite-evitable-d-une-fonction.webp\" alt=\"\u95a2\u6570\u306e\u56de\u907f\u53ef\u80fd\u306a\u4e0d\u9023\u7d9a\u6027\" class=\"wp-image-1400\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p>\u3053\u306e\u95a2\u6570\u306e\u6a2a\u65b9\u5411\u306e\u9650\u754c\u306f\u4e92\u3044\u306b\u7b49\u3057\u3044\u3067\u3059\u304c\u3001\u305d\u308c\u3089\u306f\u305d\u306e\u6642\u70b9\u3067\u306e\u95a2\u6570\u306e\u5024\u3068\u306f\u7570\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u306f\u56de\u907f\u53ef\u80fd\u306a\u4e0d\u9023\u7d9a\u6027\u3092\u793a\u3057\u307e\u3059\u3002 <\/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-ac5bdc61d377477ddcc788b7230bcfbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left. \\begin{array}{l}\\displaystyle \\lim_{x \\to a^-} f(x) =b \\\\[3ex] \\displaystyle \\lim_{x \\to a^+} f(x)=b \\end{array} \\right\\} \\ \\bm{\\longrightarrow} \\ \\lim_{x \\to a} f(x)=b\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"276\" style=\"vertical-align: 0px;\"><\/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-9f61efde161e83828572db200f128ced_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a} f(x)=b \\qquad f(a)=c\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"198\" style=\"vertical-align: -12px;\"><\/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-de211758fe99134c01f6eec8ea7c6348_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\exists \\lim_{x \\to a} f(x) \\neq f(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"135\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow\">\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/discontinuite-evitable-d-une-fonction-sans-image.webp\" alt=\"\u753b\u50cf\u306e\u306a\u3044\u95a2\u6570\u306e\u56de\u907f\u53ef\u80fd\u306a\u4e0d\u9023\u7d9a\u6027\" class=\"wp-image-1401\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p class=\"has-text-align-left\">\u524d\u306e\u4f8b\u306e\u95a2\u6570\u306b\u306f\u3001x=a \u3067\u306e\u6a2a\u65b9\u5411\u306e\u9650\u754c\u304c\u540c\u3058\u5024\u3092\u6301\u3064\u305f\u3081\u3001\u56de\u907f\u53ef\u80fd\u306a\u4e0d\u9023\u7d9a\u6027\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u3053\u306e\u70b9\u3067\u306e\u95a2\u6570\u306e\u30a4\u30e1\u30fc\u30b8\u306f\u5b58\u5728\u3057\u307e\u305b\u3093\u3002<\/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-ac5bdc61d377477ddcc788b7230bcfbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left. \\begin{array}{l}\\displaystyle \\lim_{x \\to a^-} f(x) =b \\\\[3ex] \\displaystyle \\lim_{x \\to a^+} f(x)=b \\end{array} \\right\\} \\ \\bm{\\longrightarrow} \\ \\lim_{x \\to a} f(x)=b\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"276\" style=\"vertical-align: 0px;\"><\/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-87531b3fbfb53b42e79af5a7305ffc37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a} f(x)=b \\qquad \\cancel{\\exists} \\ f(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"181\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u7167:<\/strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u6a2a\u65b9\u5411\u306e\u9650\u754c\/\">\u95a2\u6570\u306e\u6a2a\u65b9\u5411\u306e\u5236\u9650<\/a><\/span><\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"discontinuidad-inevitable-de-salto-finito\"><\/span>\u6709\u9650\u30b8\u30e3\u30f3\u30d7\u306e\u5fc5\u7136\u7684\u306a\u4e0d\u9023\u7d9a\u6027<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n<p><strong>\u907f\u3051\u3089\u308c\u306a\u3044\u6709\u9650\u30b8\u30e3\u30f3\u30d7\u306e\u4e0d\u9023\u7d9a\u6027\u306f\u3001<\/strong>\u3042\u308b\u70b9\u3067\u306e\u95a2\u6570\u306e\u6a2a\u65b9\u5411\u306e\u9650\u754c\u304c\u7b49\u3057\u304f\u306a\u3044\u3068\u304d\u306b\u3001\u305d\u306e\u70b9\u3067\u95a2\u6570\u3092\u8868\u3059\u4e0d\u9023\u7d9a\u6027\u306e\u4e00\u7a2e\u3067\u3059\u3002<\/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-66fd7a55b2fad1a91622d738925d3304_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to a^-} f(x) \\neq \\lim_{x \\to a^+} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"175\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u305f\u3068\u3048\u3070\u3001\u5b9a\u7fa9\u5909\u66f4\u70b9\u306b\u304a\u3051\u308b\u6b21\u306e\u533a\u5206\u7684\u306b\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570\u306e\u6a2a\u65b9\u5411\u306e\u9650\u754c\u306f\u7570\u306a\u308b\u305f\u3081\u3001\u95a2\u6570\u306b\u306f\u305d\u306e\u70b9\u3067\u907f\u3051\u3089\u308c\u306a\u3044\u6709\u9650\u30b8\u30e3\u30f3\u30d7\u306e\u4e0d\u9023\u7d9a\u6027\u304c\u751f\u3058\u307e\u3059\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/saut-fini-inevitable-discontinuite.webp\" alt=\"\u6709\u9650\u30b8\u30e3\u30f3\u30d7\u306e\u907f\u3051\u3089\u308c\u306a\u3044\u4e0d\u9023\u7d9a\u6027\" class=\"wp-image-1406\" width=\"275\" height=\"258\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f7173f197ec50976b07e8ab608ec4aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a^-} f(x)=b \\qquad  \\lim_{x \\to a^+} f(x)=c\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"254\" 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-66fd7a55b2fad1a91622d738925d3304_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to a^-} f(x) \\neq \\lim_{x \\to a^+} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"175\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u30bf\u30a4\u30d7\u306e\u4e0d\u9023\u7d9a\u6027\u306f\u4e00\u822c\u306b\u3001\u533a\u5206\u7684\u306b (\u307e\u305f\u306f\u533a\u5206\u7684\u306b) \u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570\u306b\u73fe\u308c\u307e\u3059\u3002<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u7167:<\/strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\">\u533a\u5206\u95a2\u6570\u306e\u9023\u7d9a\u6027<\/a><\/span><\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"discontinuidad-inevitable-de-salto-infinito\"><\/span>\u7121\u9650\u30b8\u30e3\u30f3\u30d7 \u5fc5\u7136\u306e\u65ad\u7d76<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-107\"><strong> <\/strong><\/div>\n<\/div>\n<p><strong>\u907f\u3051\u3089\u308c\u306a\u3044\u7121\u9650\u30b8\u30e3\u30f3\u30d7\u306e\u4e0d\u9023\u7d9a\u6027\u306f\u3001<\/strong>\u305d\u306e\u70b9\u3067\u306e\u6a2a\u65b9\u5411\u306e\u5236\u9650\u306e 1 \u3064\u304c\u7121\u9650\u3067\u3042\u308b\u304b\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u306b\u6a5f\u80fd\u3059\u308b\u4e0d\u9023\u7d9a\u6027\u306e\u4e00\u7a2e\u3067\u3059\u3002 <\/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-a67f3a84bbd7cc965e932b0cb681912a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to a^-} f(x) = \\pm \\infty \\qquad \\lim_{x \\to a^+} f(x)= \\pm \\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"301\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-102\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p>\u6b21\u306e\u95a2\u6570\u306e\u5de6\u9650\u306f\u5b9f\u6570\u3092\u4e0e\u3048\u307e\u3059\u304c\u3001\u53f3\u9650\u306f\u7121\u9650\u5927\u3092\u4e0e\u3048\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u95a2\u6570\u306b\u306f\u7121\u9650\u30b8\u30e3\u30f3\u30d7\u306e\u4e0d\u9023\u7d9a\u6027\u304c\u907f\u3051\u3089\u308c\u307e\u305b\u3093\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/saut-infini-discontinuite.webp\" alt=\"\u7121\u9650\u30b8\u30e3\u30f3\u30d7\u306e\u4e0d\u9023\u7d9a\" class=\"wp-image-1411\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9e12509ad0839664b52f4224f0fc2e56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a^-} f(x)=b \\qquad \\lim_{x \\to a^+} f(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"277\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-left\">\u4ee5\u4e0b\u306b\u3001\u4e21\u5074\u306e\u9650\u754c\u304c\u7121\u9650\u5927\u3092\u4e0e\u3048\u308b\u30b0\u30e9\u30d5\u95a2\u6570\u3092\u793a\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u95a2\u6570\u306b\u306f\u7121\u9650\u30b8\u30e3\u30f3\u30d7\u306e\u4e0d\u9023\u7d9a\u6027\u304c\u907f\u3051\u3089\u308c\u307e\u305b\u3093\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/discontinuite-infinie.webp\" alt=\"\u7121\u9650\u306e\u4e0d\u9023\u7d9a\u6027\" class=\"wp-image-1412\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-99099617bca8a79ef975169f06f5c14e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a^-} f(x)=-\\infty \\qquad \\lim_{x \\to a^+} f(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"301\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p>\u3053\u306e\u30bf\u30a4\u30d7\u306e\u4e0d\u9023\u7d9a\u306f\u901a\u5e38<span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u6709\u7406\u95a2\u6570\/\">\u3001\u6709\u7406 (\u307e\u305f\u306f\u5206\u6570) \u95a2\u6570<\/a><\/span>\u3067\u767a\u751f\u3057\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-tipos-de-discontinuidades\"><\/span>\u4e0d\u9023\u7d9a\u6027\u306e\u7a2e\u985e\u306b\u95a2\u3059\u308b\u89e3\u6c7a\u3055\u308c\u305f\u6f14\u7fd2<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 1 <\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-108\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n<p>\u6b21\u306e\u533a\u5206\u95a2\u6570\u306e\u70b9 x=3 \u306b\u304a\u3051\u308b\u4e0d\u9023\u7d9a\u6027\u306e\u30bf\u30a4\u30d7\u3092\u6c7a\u5b9a\u3057\u307e\u3059\u3002 <\/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-8185827ad36ab3921bb96eb5a6da21a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\left\\{ \\begin{array}{lcl} -2x+1 &amp;  \\text{si} &amp;  x\\leq 3 \\\\[2ex] 4x - 5 &amp; \\text{si} &amp; x > 3 \\end{array} \\right.&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;65&#8243; width=&#8221;232&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/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>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u95a2\u6570\u306e\u6700\u521d\u306e\u8981\u7d20\u306e\u30c9\u30e1\u30a4\u30f3\u3001<\/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-490b7f67d1b8735fc34485932796cef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"61\" style=\"vertical-align: -2px;\"><\/p>\n<p> \u30012\u679a\u76ee\u3068\u540c\u3058\u3088\u3046\u306b\u3001<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82dafeb4abb94d9f10e1603d00cc3d59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x-5\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u3001\u591a\u9805\u5f0f\u95a2\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u3059\u3079\u3066\u5b9f\u6570\u3067\u3059\u3002<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u304c\u4e0d\u9023\u7d9a\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u552f\u4e00\u306e\u70b9\u306f\u3001\u533a\u5206\u95a2\u6570\u306e\u505c\u6b62\u70b9\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u6bb5\u968e\u3067\u6a2a\u65b9\u5411\u306e\u5236\u9650\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002 <\/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-e5aa03a9198a249e6cb09793b67754f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to 3^-} f(x)=\\lim_{x \\to 3} (-2x+1) = -2\\cdot 3+1=-5\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"349\" 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-c8e29ea20c018b8936dca674ada7590a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to 3^+} f(x)=\\lim_{x \\to 3}(4x-5)=4\\cdot 3-5=7\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"308\" 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-ffa1cc3d456b55bfef8f4a5999e072e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 3^-} f(x) \\neq \\lim_{x \\to 3^+} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"174\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> x=3 \u3067\u306e 2 \u3064\u306e\u6a2a\u65b9\u5411\u306e\u5236\u9650\u306b\u3088\u308a\u3001\u7570\u306a\u308b\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u70b9 x=3 \u306f\u907f\u3051\u3089\u308c\u306a\u3044\u6709\u9650\u30b8\u30e3\u30f3\u30d7\u306e\u4e0d\u9023\u7d9a\u3067\u3059\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 2<\/h3>\n<p>\u6b21\u306e\u6709\u7406\u95a2\u6570\u304c\u305d\u306e\u9818\u57df\u306b\u5c5e\u3055\u306a\u3044\u70b9\u3067\u3069\u306e\u3088\u3046\u306a\u7a2e\u985e\u306e\u4e0d\u9023\u7d9a\u6027\u3092\u793a\u3059\u304b\u3092\u8abf\u3079\u307e\u3059\u3002 <\/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-44d5d873cde7d3365fc55943c61e78f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)= \\cfrac{x^2-4}{x+2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"109\" style=\"vertical-align: -14px;\"><\/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>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8ad6\u7406\u7684\u306b\u306f\u3001\u3053\u306e\u6f14\u7fd2\u3092\u89e3\u6c7a\u3059\u308b\u306b\u306f\u3001\u307e\u305a\u95a2\u6570\u306e\u5b9a\u7fa9\u57df\u3092\u898b\u3064\u3051\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u308c\u306f\u6709\u7406\u95a2\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u5206\u6bcd\u3092 0 \u306b\u8a2d\u5b9a\u3057\u3001\u7d50\u679c\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u304d\u307e\u3059\u3002 <\/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-24e301fa7ea2e8d9f0041192d9a84927_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"73\" style=\"vertical-align: -2px;\"><\/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-01f282abd343bbe6b83c45e54b86c6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/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-fbd5fe607cd89a42b4db6e52bc047c56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{-2\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u306f x=-2 \u3092\u9664\u304f\u3059\u3079\u3066\u306e\u70b9\u3067\u9023\u7d9a\u3068\u306a\u308b\u305f\u3081\u3001\u70b9 x=-2 \u304c\u3069\u306e\u3088\u3046\u306a\u7a2e\u985e\u306e\u4e0d\u9023\u7d9a\u3067\u3042\u308b\u304b\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u3053\u308c\u3092\u884c\u3046\u305f\u3081\u306b\u3001\u6b21\u306e\u70b9\u3067\u306e\u95a2\u6570\u306e\u9650\u754c\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/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-bf6f3ceb66dcd630224097f54365ef24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2} \\cfrac{x^2-4}{x+2} = \\cfrac{ (-2)^2-4}{-2+2}= \\cfrac{0}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"227\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u304b\u3057\u3001\u30bc\u30ed\u9593\u306e\u4e0d\u78ba\u5b9a\u6027\u306f\u30bc\u30ed\u306b\u306a\u308b\u305f\u3081\u3001\u5206\u5b50\u3068\u5206\u6bcd\u306e\u591a\u9805\u5f0f\u3092\u56e0\u6570\u5206\u89e3\u3057\u3066\u5358\u7d14\u5316\u3057\u307e\u3059\u3002<\/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-e939f4fee6ac399b046fa809daab31c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2} \\cfrac{x^2-4}{x+2}=\\lim_{x \\to -2} \\cfrac{ (x-2)\\cancel{(x+2)}}{\\cancel{x+2}}  =\\lim_{x \\to -2} (x-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"385\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6b21\u306b\u3001\u5236\u9650\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002<\/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-5e05e20f45a4d8b2fbe26bb0d3ae5091_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2} (x-2) =-2-2=-4\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"217\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u70b9 x=-2 \u306b\u304a\u3051\u308b\u95a2\u6570\u306e\u6975\u9650\u306f\u5b58\u5728\u3057\u3001-4 \u3092\u4e0e\u3048\u307e\u3059\u3002\u3067\u306f\u3001\u5b58\u5728\u3059\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3057\u3087\u3046<\/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-80b84d482e50cebc375313e005736c97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -5px;\"><\/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-c58a37ec90f203b24b790c7cfacaf2c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2)=\\cfrac{(-2)^2-4}{-2+2}= \\cfrac{4-4}{0} = \\cfrac{0}{0} \\quad \\bm{\\longrightarrow} \\quad \\cancel{\\exists} \\ f(2)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"359\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u95a2\u6570\u306e\u30a4\u30e1\u30fc\u30b8\u3092\u8a08\u7b97\u3059\u308b\u5834\u5408\u3001\u4e0d\u78ba\u5b9a\u6027 0\/0 \u306f\u5358\u7d14\u5316\u3067\u304d\u305a\u3001\u89e3\u304c\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u308c\u3067<\/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-7ee53c0d0a8e84c09c63d946334cd34b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u5b58\u5728\u3057\u306a\u3044\u3002<\/p>\n<p class=\"has-text-align-left\">\u7d50\u8ad6\u3068\u3057\u3066\u3001x=-2 \u306b\u304a\u3051\u308b\u95a2\u6570\u306e\u6975\u9650\u306f\u5b58\u5728\u3057\u307e\u3059\u304c\u3001<\/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-7ee53c0d0a8e84c09c63d946334cd34b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u3044\u3044\u3048\u3002\u3057\u305f\u304c\u3063\u3066\u3001x=-2 \u306f\u56de\u907f\u53ef\u80fd\u306a\u4e0d\u9023\u7d9a\u70b9\u3067\u3059\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 3 <\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-110\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n<p>\u6b21\u306e\u6709\u7406\u95a2\u6570\u306e\u9023\u7d9a\u6027\u3092\u5206\u6790\u3057\u307e\u3059\u3002 <\/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-59ee18262fd6f3427ebab6ceabb22868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\frac{2}{x-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"101\" 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>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u9023\u7d9a\u95a2\u6570\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3059\u308b\u306b\u306f\u3001\u307e\u305a\u305d\u306e\u5b9a\u7fa9\u57df\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3069\u306e\u70b9\u304c\u30c9\u30e1\u30a4\u30f3\u306b\u5c5e\u3057\u3066\u3044\u306a\u3044\u306e\u304b\u3092\u78ba\u8a8d\u3059\u308b\u305f\u3081\u306b\u3001\u6709\u7406\u95a2\u6570\u306e\u5206\u6bcd\u3092\u30bc\u30ed\u306b\u8a2d\u5b9a\u3057\u307e\u3059\u3002 <\/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-845b4cbd750afedb8e09b0ed6a9809c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"73\" style=\"vertical-align: 0px;\"><\/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-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=5\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\"><\/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-96a28ea816d10d62e90dd13ad1aa79c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{5\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u306f x=5 \u3092\u9664\u304f\u3059\u3079\u3066\u306e\u70b9\u3067\u9023\u7d9a\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u6642\u70b9\u3067\u306e\u9650\u754c\u3092\u8a08\u7b97\u3057\u3066\u3001x=5 \u304c\u3069\u306e\u3088\u3046\u306a\u7a2e\u985e\u306e\u4e0d\u9023\u7d9a\u6027\u3067\u3042\u308b\u304b\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/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-976747f92d549df73e0cf24ee4ff2953_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 5} \\frac{2}{x-5} = \\frac{2}{5-5} = \\frac{2}{0} = \\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"220\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6570\u5024\u3092 0 \u3067\u5272\u3063\u305f\u5024\u304c\u4e0d\u78ba\u5b9a\u3067\u3042\u308b\u3053\u3068\u306b\u6c17\u3065\u304d\u307e\u3057\u305f\u3002\u3057\u305f\u304c\u3063\u3066\u3001x=5 \u3067\u306e\u95a2\u6570\u306e\u6a2a\u65b9\u5411\u306e\u6975\u9650\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002 <\/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-98edca328c2637f8b7ae59dde1789f44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 5^{-}} \\frac{2}{x-5}=\\frac{2}{4,999-5}=\\frac{2}{-0}= \\bm{-\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"292\" 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-378f3bdf00d4375069e68f4fc8547ca0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 5^{+}} \\frac{2}{x-5}=\\frac{2}{5,001-5}=\\frac{2}{+0}=\\bm{+\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"292\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> x=5 \u3067\u306e\u95a2\u6570\u306e\u5de6\u306e\u9650\u754c\u306f\u30de\u30a4\u30ca\u30b9\u306e\u7121\u9650\u5927\u3092\u4e0e\u3048\u3001\u53f3\u306e\u9650\u754c\u306f\u30d7\u30e9\u30b9\u306e\u7121\u9650\u5927\u3092\u4e0e\u3048\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u70b9\u3067\u5c11\u306a\u304f\u3068\u3082 1 \u3064\u306e\u6a2a\u65b9\u5411\u306e\u9650\u754c\u304c\u7121\u9650\u5927\u306b\u306a\u308b\u50be\u5411\u304c\u3042\u308b\u305f\u3081\u3001\u3053\u306e\u95a2\u6570\u306b\u306f x = 5 \u3067\u7121\u9650\u30b8\u30e3\u30f3\u30d7\u306e\u4e0d\u9023\u7d9a\u6027\u304c\u907f\u3051\u3089\u308c\u307e\u305b\u3093\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 4<\/h3>\n<p>\u6b21\u306e\u30b0\u30e9\u30d5\u306b\u793a\u3055\u308c\u3066\u3044\u308b\u533a\u5206\u95a2\u6570\u306e\u4e0d\u9023\u7d9a\u70b9\u3092\u3059\u3079\u3066\u6c7a\u5b9a\u3057\u307e\u3059\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-discontinuites-de-fonctions.webp\" alt=\"\u904b\u52d5\u306b\u3088\u308a\u6a5f\u80fd\u306e\u4e0d\u9023\u7d9a\u6027\u304c\u89e3\u6c7a\u3055\u308c\u305f\" class=\"wp-image-1433\" width=\"400\" height=\"344\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\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>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u95a2\u6570\u3092\u63cf\u304f\u306b\u306f\u3001x=-2\u3001x=1\u3001x=4 \u306e\u4f4d\u7f6e\u3067\u925b\u7b46\u3092\u6301\u3061\u4e0a\u3052\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u306f\u3053\u308c\u3089 3 \u3064\u306e\u70b9\u3067\u4e0d\u9023\u7d9a\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p class=\"has-text-align-left\"> x=-2 \u3067\u306f\u3001\u5de6\u5074\u306e\u9650\u754c\u306f +\u221e \u3067\u3001\u53f3\u5074\u306e\u9650\u754c\u306f 3 \u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5074\u9762\u306e\u9650\u754c\u306e 1 \u3064\u304c\u7121\u9650\u3067\u3042\u308b\u305f\u3081\u3001\u95a2\u6570\u306b\u306f x=-2 \u3067\u7121\u9650\u30b8\u30e3\u30f3\u30d7\u306e\u4e0d\u9023\u7d9a\u6027\u304c\u907f\u3051\u3089\u308c\u307e\u305b\u3093\u3002<\/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-eff79ace33659ceb8203e6e27f38fe35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2^-} f(x) = +\\infty \\ \\neq \\ \\lim_{x \\to -2^+} f(x) = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"296\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> x=1 \u3067\u306e\u95a2\u6570\u306e\u9650\u754c\u306f 0 \u3067\u3042\u308a\u3001\u4e00\u65b9\u3001x=1 \u3067\u306e\u95a2\u6570\u306e\u5024\u306f 2 \u306b\u7b49\u3057\u3044\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u95a2\u6570\u306f x=1 \u3067\u56de\u907f\u53ef\u80fd\u306a\u4e0d\u9023\u7d9a\u6027\u3092\u793a\u3057\u307e\u3059\u3002 <\/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-3a616cc5210984ffeed3525a219dd53a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1^-} f(x) =   \\lim_{x \\to 1^+} f(x) = 0 \\ \\bm{\\longrightarrow} \\ \\lim_{x \\to 1} f(x) = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"350\" 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-9a3aea29db1a67d08d91d510033ffd1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1} f(x) =  0 \\neq  f(1) = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"187\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> x = 4 \u3067\u306f\u3001\u5de6\u5074\u306e\u9650\u754c\u306f -3 \u3067\u3001\u53f3\u5074\u306e\u9650\u754c\u306f 1 \u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u8fba\u306e\u9650\u754c\u306f\u7570\u306a\u308a\u3001\u3069\u3061\u3089\u3082\u7121\u9650\u5927\u3092\u4e0e\u3048\u306a\u3044\u305f\u3081\u3001\u95a2\u6570\u306b\u306f\u5fc5\u7136\u7684\u306b x =4 \u3067\u6709\u9650\u30b8\u30e3\u30f3\u30d7\u306e\u4e0d\u9023\u7d9a\u6027\u304c\u751f\u3058\u307e\u3059\u3002 <\/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-b758745a987f927350b2d885009c3a87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 4^-} f(x) = -3 \\ \\neq \\ \\lim_{x \\to 4^+} f(x) = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"265\" 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\">\u6f14\u7fd2 5<\/h3>\n<p>\u6b21\u306e\u30b0\u30e9\u30d5\u3067\u8868\u3055\u308c\u308b\u95a2\u6570\u306e\u3059\u3079\u3066\u306e\u6f38\u8fd1\u7dda\u3068\u4e0d\u9023\u7d9a\u70b9\u3092\u898b\u3064\u3051\u307e\u3059\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-types-de-discontinuites-d-une-fonction.webp\" alt=\"\u95a2\u6570\u306e\u4e0d\u9023\u7d9a\u6027\u306e\u7a2e\u985e\u306b\u95a2\u3059\u308b\u6f14\u7fd2\u3092\u89e3\u6c7a\u3057\u307e\u3057\u305f\" class=\"wp-image-1435\" width=\"537\" height=\"453\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\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>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"><strong><span style=\"text-decoration: underline;\">\u6f38\u8fd1\u7dda<\/span><\/strong><\/p>\n<p class=\"has-text-align-left\">\u3053\u306e\u95a2\u6570\u306f\u5782\u76f4\u7dda x=3 \u306b\u975e\u5e38\u306b\u8fd1\u3044\u3067\u3059\u304c\u3001\u63a5\u89e6\u3059\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3055\u3089\u306b\u3001x=3 \u3067\u306e\u5de6\u5074\u306e\u6a2a\u9650\u754c\u306f +\u221e\u3001\u53f3\u5074\u306e\u6a2a\u9650\u754c\u306f -\u221e \u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001x=3 \u306f\u5782\u76f4\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u306b\u306a\u308a\u307e\u3059\u3002<\/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-89bdb1598b6153cec4e9efce7b0927b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 3^-} f(x)=+\\infty \\qquad \\lim_{x \\to 3^+} f(x)=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"300\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u3001\u540c\u3058\u3053\u3068\u304c\u6c34\u5e73\u7dda y=-1 \u3067\u3082\u8d77\u3053\u308a\u3001\u95a2\u6570\u306f y=-1 \u306b\u975e\u5e38\u306b\u8fd1\u3065\u304d\u307e\u3059\u304c\u3001\u305d\u308c\u3092\u6a2a\u5207\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3055\u3089\u306b\u3001x \u304c +\u221e \u304a\u3088\u3073 -\u221e \u306b\u8fd1\u3065\u304f\u3068\u304d\u306e\u95a2\u6570\u306e\u9650\u754c\u306f -1 \u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001y=-1 \u306f\u6c34\u5e73\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u306b\u306a\u308a\u307e\u3059\u3002<\/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-d0f0ee09aaa4a3bfa4fcb77ecc84640a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} f(x)=-1 \\qquad \\lim_{x \\to -\\infty} f(x)=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"297\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong><span style=\"text-decoration: underline;\">\u4e0d\u9023\u7d9a\u6027<\/span><\/strong><\/p>\n<p class=\"has-text-align-left\">x=6 \u3067\u306f\u3001\u958b\u3044\u305f\u70b9\u304c\u3042\u308b\u305f\u3081\u3001\u95a2\u6570\u306f\u4e2d\u65ad\u3055\u308c\u307e\u3059\u3002 x \u304c 6 \u306b\u8fd1\u3065\u304f\u3068\u304d\u306e\u9650\u754c\u306f -1.4 \u3067\u3059\u304c\u3001f(6)=1 \u306b\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5236\u9650\u306e\u5024\u304c\u95a2\u6570\u306e\u5024\u3068\u4e00\u81f4\u3057\u306a\u3044\u305f\u3081\u3001\u95a2\u6570\u306b\u306f x=6 \u3067\u56de\u907f\u53ef\u80fd\u306a\u4e0d\u9023\u7d9a\u6027\u304c\u3042\u308a\u307e\u3059\u3002 <\/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-33612be383c71fea04c8c886710f7f10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left. \\begin{array}{l} \\displaystyle \\lim_{x \\to 6^-} f(x)=-1,4\\\\[3ex] \\displaystyle \\lim_{x \\to 6^+} f(x)=-1,4 \\end{array} \\right\\} \\bm{\\longrightarrow} \\lim_{x \\to 6} f(x)=-1,4\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"326\" style=\"vertical-align: 0px;\"><\/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-647b9aea6cc8b605d7e8bc7d5e83ee64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 6} f(x)=-1,4 \\neq f(6)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"217\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> x=-3 \u3067\u306f\u3001\u6a2a\u65b9\u5411\u306e\u9650\u754c\u306f\u4e00\u81f4\u305b\u305a\u3001\u3069\u308c\u3082\u7121\u9650\u5927\u3092\u4e0e\u3048\u307e\u305b\u3093\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u306b\u306f x=-3 \u3067\u6709\u9650\u30b8\u30e3\u30f3\u30d7\u306e\u4e0d\u9023\u7d9a\u6027\u304c\u907f\u3051\u3089\u308c\u307e\u305b\u3093\u3002<\/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-3f7d2a2c7abbc525adfcc7576b449f1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -3^-} f(x)=-2 \\neq \\lim_{x \\to -3^+} f(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"275\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u3053\u306e\u6642\u70b9\u3067\u5c11\u306a\u304f\u3068\u3082 1 \u3064\u306e\u6a2a\u65b9\u5411\u306e\u9650\u754c\u304c\u7121\u9650\u5927\u306b\u306a\u308b\u305f\u3081\u3001\u3053\u306e\u95a2\u6570\u306b\u306f x = 3 \u3067\u7121\u9650\u30b8\u30e3\u30f3\u30d7\u306e\u4e0d\u9023\u7d9a\u6027\u304c\u907f\u3051\u3089\u308c\u307e\u305b\u3093\u3002 <\/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-89bdb1598b6153cec4e9efce7b0927b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 3^-} f(x)=+\\infty \\qquad \\lim_{x \\to 3^+} f(x)=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"300\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u3053\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306a\u7a2e\u985e\u306e\u4e0d\u9023\u7d9a\u6027\u304c\u5b58\u5728\u3059\u308b\u304b\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u3042\u3089\u3086\u308b\u7a2e\u985e\u306e\u4e0d\u9023\u7d9a\u6027\u306e\u4f8b\u3092\u78ba\u8a8d\u3067\u304d\u3001\u95a2\u6570\u306e\u4e0d\u9023\u7d9a\u6027\u306e\u7a2e\u985e\u306b\u95a2\u3059\u308b\u89e3\u7b54\u6e08\u307f\u306e\u6f14\u7fd2\u3092\u4f7f\u7528\u3057\u3066\u7df4\u7fd2\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u3042\u3089\u3086\u308b\u7a2e\u985e\u306e\u4e0d\u9023\u7d9a\u6027\u3068\u306f\u4f55\u3067\u3059\u304b? &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e4%b8%8d%e9%80%a3%e7%b6%9a%e6%80%a7%e3%81%ae%e7%a8%ae%e9%a1%9e\/\"> <span class=\"screen-reader-text\">\u4e0d\u9023\u7d9a\u6027\u306e\u7a2e\u985e<\/span> \u3082\u3063\u3068\u8aad\u3080 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[11],"tags":[],"class_list":["post-23","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized 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