{"id":375,"date":"2023-07-04T03:00:17","date_gmt":"2023-07-04T03:00:17","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e7%84%a1%e9%99%90%e9%96%93%e3%81%ae%e4%b8%8d%e5%ae%9a%e7%84%a1%e9%99%90-%e2%88%9e-%e2%88%9e\/"},"modified":"2023-07-04T03:00:17","modified_gmt":"2023-07-04T03:00:17","slug":"%e7%84%a1%e9%99%90%e9%96%93%e3%81%ae%e4%b8%8d%e5%ae%9a%e7%84%a1%e9%99%90-%e2%88%9e-%e2%88%9e","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e7%84%a1%e9%99%90%e9%96%93%e3%81%ae%e4%b8%8d%e5%ae%9a%e7%84%a1%e9%99%90-%e2%88%9e-%e2%88%9e\/","title":{"rendered":"\u7121\u9650\u9593\u306e\u7121\u9650\u4e0d\u78ba\u5b9a\u6027 (\u221e\/\u221e)"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u7121\u9650\u5927\u9593\u306e\u4e0d\u78ba\u5b9a\u6027\u306e\u7121\u9650\u5927(\u221e\/\u221e)\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u591a\u9805\u5f0f\u3001\u6839\u6570\u3001\u6307\u6570\u95a2\u6570\u306a\u3069\u3001\u3042\u3089\u3086\u308b\u7a2e\u985e\u306e\u95a2\u6570\u3092\u4f7f\u7528\u3057\u305f\u3053\u306e\u4e0d\u6c7a\u5b9a\u306e\u4f8b\u304c\u898b\u3064\u304b\u308a\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u7121\u9650\u9593\u306e\u7121\u9650\u4e0d\u5b9a\u3092\u4e0e\u3048\u308b\u9650\u754c\u3092\u6bb5\u968e\u7684\u306b\u89e3\u6c7a\u3059\u308b\u6f14\u7fd2\u3067\u30c8\u30ec\u30fc\u30cb\u30f3\u30b0\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-resolver-la-indeterminacion-infinito-entre-infinito\"><\/span>\u7121\u9650\u9593\u306e\u7121\u9650\u4e0d\u78ba\u5b9a\u6027\u3092\u89e3\u6c7a\u3059\u308b\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u95a2\u6570\u306e\u6975\u9650\u304c\u7121\u9650\u5927\u3092\u7121\u9650\u5927\u3067\u5272\u3063\u305f\u3068\u304d\u3001\u305d\u308c\u306f\u4e0d\u78ba\u5b9a\u6027 (\u307e\u305f\u306f\u4e0d\u78ba\u5b9a\u5f62\u5f0f) \u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<strong>\u7121\u9650\u5927\u9593\u306e\u4e0d\u78ba\u5b9a\u6027\u3092\u7121\u9650\u5927\u306b\u3059\u308b\u95a2\u6570\u306e\u6975\u9650\u3092\u89e3\u304f\u306b\u306f\u3001<\/strong>\u5206\u5b50\u591a\u9805\u5f0f\u306e\u6b21\u6570\u3092\u5206\u6bcd\u591a\u9805\u5f0f\u306e\u6b21\u6570\u3068\u6bd4\u8f03\u3059\u308b\u5fc5\u8981\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-77419fd05960300c6e2cd6158cd04e69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\frac{a_nx^r+a_{n-1}x^{r-1}+a_{n-2}x^{r-2}+\\dots}{b_nx^s+b_{n-1}x^{s-1}+b_{n-2}x^{s-2}+\\dots}=\\frac{+\\infty}{+\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"375\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p>\u4e0d\u78ba\u5b9a\u6027\u7121\u9650\u3092\u7121\u9650\u3067\u5272\u3063\u305f\u7d50\u679c\u306f\u3001\u5206\u6570\u306e\u5206\u5b50\u306e\u6b21\u6570\u3068\u5206\u6bcd\u306e\u6b21\u6570\u306b\u3088\u3063\u3066\u7570\u306a\u308a\u307e\u3059\u3002<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;border:\">\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\">\u5206\u5b50\u591a\u9805\u5f0f\u306e\u6b21\u6570\u304c\u5206\u6bcd\u591a\u9805\u5f0f\u306e\u6b21\u6570\u3088\u308a\u5c0f\u3055\u3044\u5834\u5408\u3001\u4e0d\u78ba\u5b9a\u6027\u306e\u7121\u9650\u5927\u3092\u7121\u9650\u5927\u3067\u5272\u3063\u305f\u5024<strong><u style=\"text-decoration-color:#FF9B28;\">\u306f\u30bc\u30ed\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/u><\/strong><\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\">\u5206\u5b50\u591a\u9805\u5f0f\u306e\u6b21\u6570\u304c\u5206\u6bcd\u591a\u9805\u5f0f\u306e\u6b21\u6570\u3068\u7b49\u3057\u3044\u5834\u5408\u3001\u7121\u9650\u5927\u306b\u308f\u305f\u308b\u7121\u9650\u4e0d\u78ba\u5b9a\u6027<strong><u style=\"text-decoration-color:#FF9B28;\">\u306f 2 \u3064\u306e\u591a\u9805\u5f0f\u306e\u4e3b\u8981\u4fc2\u6570\u306e\u5546\u306b\u306a\u308a\u307e\u3059\u3002<\/u><\/strong><\/span><\/li>\n<li><span style=\"color:#101010;font-weight: normal;\">\u5206\u5b50\u591a\u9805\u5f0f\u306e\u6b21\u6570\u304c\u5206\u6bcd\u591a\u9805\u5f0f\u306e\u6b21\u6570\u3088\u308a\u5927\u304d\u3044\u5834\u5408\u3001\u7121\u9650\u5927\u9593\u306e\u4e0d\u78ba\u5b9a\u6027\u306e\u7121\u9650\u5927\u306f<strong><u style=\"text-decoration-color:#FF9B28;\">\u591a\u304b\u308c\u5c11\u306a\u304b\u308c\u7121\u9650\u5927\u3092<\/u><\/strong>\u4e0e\u3048\u307e\u3059 (\u7b26\u53f7\u306f 2 \u3064\u306e\u591a\u9805\u5f0f\u306e\u4e3b\u9805\u306b\u4f9d\u5b58\u3057\u307e\u3059)\u3002<\/span> <\/li>\n<\/ol>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2c969e4b99985b44006e57d554ff0247_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to \\pm \\infty}}\\frac{a_nx^r+a_{n-1}x^{r-1}+a_{n-2}x^{r-2}+\\dots}{b_nx^s+b_{n-1}x^{s-1}+b_{n-2}x^{s-2}+\\dots}=\\left\\{ \\begin{array}{lcl} 0 &amp; \\text{si} &amp; r<s \\\\[3ex]=&quot;&quot; \\cfrac{a_n}{b_n}=&quot;&quot; &amp;=&quot;&quot; \\text{si}=&quot;&quot; r=&quot;s&quot; \\\\[5ex]=&quot;&quot; \\pm=&quot;&quot; \\infty=&quot;&quot;>s \\end{array}\\right.&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;139&#8243; width=&#8221;767&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-indeterminaciones-infinito-entre-infinito\"><\/span>\u7121\u9650\u9593\u306e\u7121\u9650\u4e0d\u5b9a\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5404\u30b1\u30fc\u30b9\u306e\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u898b\u3066\u3001\u7121\u9650\u9593\u306e\u4e0d\u5b9a\u5f62\u7121\u9650\u304c\u3069\u306e\u3088\u3046\u306b\u89e3\u6c7a\u3055\u308c\u308b\u304b\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u5206\u5b50\u306e\u6b21\u6570\u304c\u5206\u6bcd\u306e\u6b21\u6570\u3088\u308a\u5c0f\u3055\u3044<\/h3>\n<p>\u4e0a\u3067\u898b\u305f\u3088\u3046\u306b\u3001\u5206\u5b50\u591a\u9805\u5f0f\u306e\u6b21\u6570\u304c\u5206\u6bcd\u591a\u9805\u5f0f\u306e\u6b21\u6570\u3088\u308a\u5c0f\u3055\u3044\u5834\u5408\u3001\u7121\u9650\u5927\u9593\u306e\u7121\u9650\u4e0d\u5b9a\u6975\u9650\u306f\u5e38\u306b 0 \u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h4 class=\"wp-block-heading\">\u4f8b 1:<\/h4>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b4e5e0058ab08d743a6dc18587912a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{6x^2-5}{x^3+1} = \\cfrac{6(+\\infty)^2}{(+\\infty)^3} = \\cfrac{+\\infty}{+\\infty}= \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"293\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5206\u5b50\u306e\u591a\u9805\u5f0f\u306f 2 \u6b21\u3067\u3042\u308a\u3001\u5206\u6bcd\u306e\u591a\u9805\u5f0f\u306f 3 \u6b21\u3067\u3042\u308b\u305f\u3081\u3001\u6975\u9650\u306e\u89e3\u306f 0 \u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h4 class=\"wp-block-heading\">\u4f8b 2:<\/h4>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7b7cb8798b808542e53a1caa8fcb9ee5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -\\infty} \\frac{-7x}{2x^4+3x^2}=\\frac{-7\\cdot (-\\infty)}{2(-\\infty)^4}=\\frac{+\\infty}{+\\infty}= \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"328\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5206\u5b50\u306e\u591a\u9805\u5f0f\u95a2\u6570\u306f 1 \u6b21\u3067\u3059\u304c\u3001\u5206\u6bcd\u306e\u95a2\u6570\u306f 4 \u6b21\u3067\u3042\u308b\u305f\u3081\u3001\u8ca0\u306e\u7121\u9650\u5927\u306e\u5236\u9650\u306f 0 \u3067\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u5206\u5b50\u306e\u6b21\u6570\u304c\u5206\u6bcd\u306e\u6b21\u6570\u306b\u7b49\u3057\u3044<\/h3>\n<p>\u5206\u5b50\u591a\u9805\u5f0f\u306e\u6b21\u6570\u304c\u5206\u6bcd\u591a\u9805\u5f0f\u306e\u6b21\u6570\u3068\u7b49\u3057\u3044\u5834\u5408\u3001\u4e0d\u5b9a\u9650\u754c\u7121\u9650\u00d7\u7121\u9650\u306f\u30012 \u3064\u306e\u591a\u9805\u5f0f\u306e\u5148\u982d\u4fc2\u6570 (\u9ad8\u6b21\u9805\u306e\u4fc2\u6570) \u3092\u9664\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002<\/p>\n<h4 class=\"wp-block-heading\">\u4f8b 3:<\/h4>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6c21a5f7720fd6be40b043d30f904941_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{4x^2+1}{2x^2-5} = \\cfrac{4(+\\infty)^2}{2(+\\infty)^2}= \\cfrac{+\\infty}{+\\infty} =\\cfrac{4}{2} = \\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"327\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u5834\u5408\u30012 \u3064\u306e\u591a\u9805\u5f0f\u306f 2 \u6b21\u3067\u3042\u308b\u305f\u3081\u3001\u3088\u308a\u9ad8\u6b21\u306e\u9805\u306e\u4fc2\u6570\u3092\u9664\u7b97\u3057\u3066\u6b63\u306e\u7121\u9650\u5927\u3067\u306e\u6975\u9650\u3092\u898b\u3064\u3051\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<h4 class=\"wp-block-heading\">\u4f8b 4:<\/h4>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6e019743989a25f2cfa1c1dd1aa718b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -\\infty} \\cfrac{2x+1}{5x+3} = \\cfrac{2(-\\infty)}{5(-\\infty)}= \\cfrac{-\\infty}{-\\infty} =\\cfrac{\\bm{2}}{\\bm{5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"280\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> x \u304c\u7121\u9650\u5927\u3092\u30de\u30a4\u30ca\u30b9\u3059\u308b\u50be\u5411\u304c\u3042\u308b\u3068\u304d\u304c\u9650\u754c\u3067\u3059\u304c\u3001\u7121\u9650\u5927\u9593\u306e\u7121\u9650\u4e0d\u78ba\u5b9a\u6027\u3082\u540c\u69d8\u306b\u89e3\u6c7a\u3055\u308c\u307e\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u5206\u5b50\u306e\u6b21\u6570\u304c\u5206\u6bcd\u306e\u6b21\u6570\u3088\u308a\u5927\u304d\u3044<\/h3>\n<p>\u5206\u5b50\u591a\u9805\u5f0f\u306e\u6b21\u6570\u304c\u5206\u6bcd\u591a\u9805\u5f0f\u306e\u6b21\u6570\u3088\u308a\u5927\u304d\u3044\u5834\u5408\u3001\u7121\u9650\u5927\u9593\u306e\u7121\u9650\u5927\u306e\u4e0d\u5b9a\u5f62\u306f\u5e38\u306b\u7121\u9650\u5927\u3092\u4e0e\u3048\u3001\u7121\u9650\u5927\u306e\u7b26\u53f7\u306f 2 \u3064\u306e\u591a\u9805\u5f0f\u306e\u9ad8\u6b21\u9805\u306b\u3088\u3063\u3066\u6c7a\u307e\u308a\u307e\u3059\u3002<\/p>\n<h4 class=\"wp-block-heading\">\u4f8b 5:<\/h4>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-36bee41554444ea88e0bc4f6d0dbf75a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{x^2+7}{x-2} = \\cfrac{(+\\infty)^2}{+\\infty} = \\cfrac{+\\infty}{+\\infty} = \\bm{+\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"297\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u5206\u5b50\u306e\u95a2\u6570\u306f\u5206\u6bcd\u306e\u95a2\u6570\u3088\u308a\u3082\u9ad8\u3044\u6b21\u6570\u3092\u6301\u3063\u3066\u3044\u308b\u305f\u3081\u3001\u7121\u9650\u5927\u306e\u4e0d\u78ba\u5b9a\u6027\u7121\u9650\u5927\u306f\u7121\u9650\u5927\u3092\u4e0e\u3048\u307e\u3059\u3002\u307e\u305f\u3001\u3053\u306e\u5834\u5408\u3001\u5206\u5b50\u3068\u5206\u6bcd\u306e\u4e21\u65b9\u304c\u6b63\u306e\u7121\u9650\u5927\u306b\u306a\u308b\u305f\u3081\u3001\u5236\u9650\u306e\u7d50\u679c\u3082\u6b63\u306b\u306a\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<h4 class=\"wp-block-heading\">\u4f8b6:<\/h4>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-de6d4de74f4fe69e45ce1a55fcb8c7d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -\\infty} \\cfrac{3x^2+2x-5}{7x+1} = \\cfrac{3(-\\infty)^2}{7(-\\infty)}=\\cfrac{3(+\\infty)}{-\\infty}}= \\cfrac{+\\infty}{-\\infty}= \\bm{-\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"436\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u554f\u984c\u3067\u306f\u3001\u4e8c\u4e57\u9805\u306f\u3044\u305a\u308c\u3082\u6b63\u3067\u3042\u308b\u305f\u3081\u3001\u5206\u5b50\u304b\u3089\u306f\u6b63\u306e\u7121\u9650\u5927\u304c\u5f97\u3089\u308c\u307e\u3059\u304c\u3001\u5206\u6bcd\u304b\u3089\u306f\u8ca0\u306e\u7121\u9650\u5927\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6b63\u3092\u8ca0\u3067\u5272\u3063\u305f\u5024\u306f\u8ca0\u306b\u7b49\u3057\u3044\u305f\u3081\u3001\u7d50\u679c\u306e\u5236\u9650\u306f\u8ca0\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-infinito-entre-infinito-con-raices\"><\/span>\u7121\u9650\u3068\u6839\u306e\u9593\u306e\u7121\u9650\u4e0d\u78ba\u5b9a\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u591a\u9805\u5f0f\u95a2\u6570\u304c\u3042\u308b\u5834\u5408\u306b\u3001\u7121\u9650\u9593\u306e\u7121\u9650\u4e0d\u78ba\u5b9a\u6027\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u2026\u6839\u304c\u3042\u308b\u5834\u5408\u3001\u7121\u9650\u306f\u7121\u9650\u3067\u3069\u308c\u3060\u3051\u9664\u7b97\u3055\u308c\u308b\u3067\u3057\u3087\u3046\u304b?<\/p>\n<p><strong>\u7121\u7406\u95a2\u6570 (\u6839\u306e\u3042\u308b\u95a2\u6570) \u306e\u6b21\u6570\u306f\u3001<\/strong>\u4e3b\u9805\u306e\u6b21\u6570\u3068\u6839\u53f7\u306e\u6307\u6570\u3068\u306e\u5546\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-ffc00917d2cc316211a57feafdddd0d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt[\\color{red}\\bm{m}\\color{black}]{a_nx^{\\color{blue}\\bm{n}\\color{black}}+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\\dots} \\ \\longrightarrow \\ \\text{grado}=\\cfrac{\\color{blue}\\bm{n}\\color{black}}{\\color{red}\\bm{m}\\color{black}}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"580\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<strong>\u6839\u3092\u6301\u3064\u95a2\u6570\u306e\u6975\u9650\u306b\u3088\u3063\u3066 infinity \u9593\u306e\u4e0d\u78ba\u5b9a\u6027\u304c\u751f\u3058\u308b<\/strong>\u5834\u5408\u3001\u4e0a\u3067\u8aac\u660e\u3057\u305f\u306e\u3068\u540c\u3058\u30eb\u30fc\u30eb\u3092\u5206\u5b50\u3068\u5206\u6bcd\u306e\u6b21\u6570\u306b\u9069\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u6839\u3092\u6301\u3064\u591a\u9805\u5f0f\u306e\u6b21\u6570\u306f\u7570\u306a\u308b\u65b9\u6cd5\u3067\u8a08\u7b97\u3055\u308c\u308b\u3053\u3068\u3092\u8003\u616e\u306b\u5165\u308c\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<p>\u6839\u53f7\u3092\u4f7f\u7528\u3057\u305f\u95a2\u6570\u306e\u7121\u9650\u5927\u3078\u306e\u5236\u9650\u306e\u6b21\u306e\u4f8b\u3092\u898b\u3066\u304f\u3060\u3055\u3044\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-b93ef0d623e6904538b361f5d6f1ef9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\frac{4x^2+11}{\\sqrt{x^8-3x^2-5}}=\\frac{4(+\\infty)^2}{\\sqrt{(+\\infty)^8}}=\\frac{+\\infty}{+\\infty}=\\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"354\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p>\u5206\u5b50\u306e\u6b21\u6570\u306f 2\u3001\u5206\u6bcd\u306e\u6b21\u6570\u306f 4 (8\/2=4) \u3067\u3042\u308a\u3001\u5206\u5b50\u306e\u6b21\u6570\u304c\u5206\u6bcd\u306e\u6b21\u6570\u3088\u308a\u5c0f\u3055\u3044\u305f\u3081\u3001\u5236\u9650\u306f 0 \u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u4e00\u65b9\u3001\u5206\u5b50\u3068\u5206\u6bcd\u306e\u6b21\u6570\u304c\u7b49\u3057\u3044\u5834\u5408\u3001\u4e0d\u5b9a\u6975\u9650\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u6839\u53f7\u3067\u4e3b\u4fc2\u6570\u3092\u53d6\u5f97\u3059\u308b\u5fc5\u8981\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-130d73020be7d3969b22ecd4381ccf8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\frac{6x-5}{\\sqrt{9x^2+2x}}=\\frac{6(+\\infty)}{\\sqrt{9(+\\infty)^2}}=\\frac{+\\infty}{+\\infty}=\\frac{6}{\\sqrt{9}}=\\frac{6}{3}=\\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"420\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-infinito-entre-infinito-con-funciones-exponenciales\"><\/span>\u7121\u9650\u3068\u6307\u6570\u95a2\u6570\u9593\u306e\u7121\u9650\u4e0d\u78ba\u5b9a\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u5f8c\u306b\u3001\u7121\u9650\u5927\u306e\u4e0d\u78ba\u5b9a\u5546\u306e\u30b1\u30fc\u30b9\u3092\u7814\u7a76\u3059\u308b\u3060\u3051\u3067\u6e08\u307f\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u7121\u9650\u5927\u3068\u6307\u6570\u95a2\u6570\u306e\u9593\u306e\u7121\u9650\u4e0d\u78ba\u5b9a\u6027\u306f\u3069\u306e\u304f\u3089\u3044\u306b\u306a\u308b\u306e\u304b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002<\/p>\n<p>\u6307\u6570\u95a2\u6570\u306e\u5897\u52a0\u306f\u591a\u9805\u5f0f\u95a2\u6570\u306e\u5897\u52a0\u3088\u308a\u3082\u306f\u308b\u304b\u306b\u5927\u304d\u3044\u305f\u3081\u3001<strong>\u6307\u6570\u95a2\u6570\u306e\u6b21\u6570\u304c\u591a\u9805\u5f0f\u95a2\u6570\u306e\u6b21\u6570\u3088\u308a\u3082\u5927\u304d\u3044\u3053\u3068\u3092\u8003\u616e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/strong><\/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-49d708f83c6876b3cdb6d884ab7b6a23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{exponencial}>\\text{polinomio}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;16&#8243; width=&#8221;192&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u7121\u9650\u4e0d\u5b9a\u6027\u3092\u7121\u9650\u3067\u5272\u3063\u305f\u7d50\u679c\u304c\u6307\u6570\u95a2\u6570\u306e\u6975\u9650\u306b\u8d77\u56e0\u3059\u308b\u5834\u5408\u306f\u3001\u5206\u5b50\u3068\u5206\u6bcd\u306e\u6b21\u6570\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u305f\u306e\u3068\u540c\u3058\u898f\u5247\u3092\u9069\u7528\u3059\u308b\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u304c\u3001\u6307\u6570\u95a2\u6570\u306f\u591a\u9805\u5f0f\u3088\u308a\u9ad8\u6b21\u3067\u3042\u308b\u3053\u3068\u3092\u8003\u616e\u3057\u3066\u304f\u3060\u3055\u3044\u3002 \u3002<\/p>\n<p>\u3055\u3089\u306b\u3001\u5272\u308a\u7b97\u306e\u5206\u5b50\u3068\u5206\u6bcd\u306b\u6307\u6570\u95a2\u6570\u304c\u3042\u308b\u5834\u5408\u3001\u5e95\u304c\u5927\u304d\u3044\u6307\u6570\u95a2\u6570\u306e\u6b21\u6570\u304c\u9ad8\u304f\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-50f9e93066ce9e76b76ef6c7a72a9fad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\frac{7x^5+6x^3-4x}{4^x}=\\frac{7(+\\infty)^5}{4^{+\\infty}}=\\frac{+\\infty}{+\\infty}=\\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"350\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u5834\u5408\u3001\u5206\u6bcd\u306f\u6307\u6570\u95a2\u6570\u3067\u5f62\u6210\u3055\u308c\u308b\u305f\u3081\u3001\u5206\u5b50\u3088\u308a\u3082\u9ad8\u6b21\u306b\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u7121\u9650\u9593\u306e\u4e0d\u5b9a\u5f62\u7121\u9650\u306f\u6d88\u6ec5\u3059\u308b\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-indeterminacion-infinito-entre-infinito\"><\/span>\u7121\u9650\u9593\u306e\u7121\u9650\u4e0d\u78ba\u5b9a\u6027\u306e\u6f14\u7fd2\u3092\u89e3\u6c7a\u3057\u307e\u3057\u305f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 1<\/h3>\n<p>\u6b21\u306e\u6709\u7406\u95a2\u6570\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-cf1cd4bc84c0a321db33330a58a89ae4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to +\\infty} \\cfrac{6x-5}{x^2-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"101\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u6975\u9650\u3092\u8a08\u7b97\u3059\u308b\u3068\u3001\u7121\u9650\u5927\u9593\u306e\u7121\u9650\u4e0d\u78ba\u5b9a\u6027\u304c\u5f97\u3089\u308c\u307e\u3059\u304c\u3001\u5206\u5b50\u306e\u6b21\u6570\u304c\u5206\u6bcd\u306e\u6b21\u6570\u3088\u308a\u3082\u5c0f\u3055\u3044\u305f\u3081\u3001\u4e0d\u78ba\u5b9a\u6975\u9650\u306f\u30bc\u30ed\u306b\u7b49\u3057\u304f\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-08cb59f29e9be213c6cf5f22f796b132_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{6x-5}{x^2-1} = \\cfrac{6(+\\infty)}{(+\\infty)^2} = \\cfrac{+\\infty}{+\\infty}= \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"278\" style=\"vertical-align: -17px;\"><\/p>\n<\/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\u4e0d\u5b9a\u6975\u9650\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-02dd4897e57603625223d03f893f78c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to +\\infty} \\cfrac{x^3+4x-1}{5x^2-3x+4}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"149\" 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\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u6975\u9650\u3092\u8a08\u7b97\u3057\u3088\u3046\u3068\u3059\u308b\u3068\u3001\u4e0d\u78ba\u5b9a\u6027 \u221e\/\u221e \u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u5206\u5b50\u591a\u9805\u5f0f\u306e\u6b21\u6570\u306f\u5206\u6bcd\u591a\u9805\u5f0f\u306e\u6b21\u6570\u3088\u308a\u5927\u304d\u3044\u305f\u3081\u3001\u4e0d\u5b9a\u6975\u9650\u306f\u30d7\u30e9\u30b9\u7121\u9650\u5927\u306b\u7b49\u3057\u304f\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-72be3fb247787c715fa772abbf1df242_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{x^3+4x-1}{5x^2-3x+4} = \\cfrac{(+\\infty)^3}{5(+\\infty)^2} = \\cfrac{+\\infty}{+\\infty}= \\bm{+\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"356\" style=\"vertical-align: -17px;\"><\/p>\n<\/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>\u6b21\u306e\u6975\u9650\u3092\u7121\u9650\u5927\u3067\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-f2459122cc1d9e723b3f78d858c48fe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{-4x^2+3}{3x+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"130\" 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\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u3053\u306e\u5236\u9650\u306b\u3088\u308a\u3001\u30d7\u30e9\u30b9\u7121\u9650\u5927\u306e\u9593\u306b\u4e0d\u78ba\u5b9a\u30de\u30a4\u30ca\u30b9\u7121\u9650\u5927\u304c\u751f\u3058\u307e\u3059\u3002\u5206\u5b50\u306e\u6b21\u6570\u306f\u5206\u6bcd\u306e\u6b21\u6570\u3088\u308a\u5927\u304d\u3044\u305f\u3081\u3001\u4e0d\u5b9a\u6975\u9650\u306f\u30d7\u30e9\u30b9\u7121\u9650\u5927\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u9664\u7b97\u306f\u8ca0\u306e\u7121\u9650\u5927\u00d7\u6b63\u306e\u7121\u9650\u5927\u3067\u3042\u308b\u305f\u3081\u3001\u7d50\u679c\u306f\u30de\u30a4\u30ca\u30b9\u7121\u9650\u5927\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-a446d2cb568ab87f57eb43614c7727e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{-4x^2+3}{3x+1} = \\cfrac{-4(+\\infty)^2}{3(+\\infty)} =\\cfrac{-4(+\\infty)}{+\\infty}= \\cfrac{-\\infty}{+\\infty}= \\bm{-\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"460\" style=\"vertical-align: -17px;\"><\/p>\n<\/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\u4e0d\u5b9a\u6975\u9650\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-08b74c12124842886ef576ef8c4eeb1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{5x+8}{-5x+2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"115\" 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\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u3053\u306e\u554f\u984c\u3067\u306f\u3001\u7121\u9650\u5927\u306b\u308f\u305f\u308b\u7121\u9650\u4e0d\u5b9a\u5f62\u5f0f\u306f\u3001\u540c\u3058\u6b21\u6570\u306e 2 \u3064\u306e\u591a\u9805\u5f0f\u306e\u5546\u304b\u3089\u5f97\u3089\u308c\u308b\u305f\u3081\u3001\u4e0d\u5b9a\u6975\u9650\u306e\u7d50\u679c\u306f\u3001\u305d\u308c\u3089\u306e\u4e3b\u4fc2\u6570\u306e\u9664\u7b97\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-dc2fb0ed175e50d56e670681c136cd17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{5x+8}{-5x+2} = \\cfrac{5(+\\infty)}{-5(+\\infty)} = \\cfrac{+\\infty}{-\\infty}=\\cfrac{5}{-5}= \\bm{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"367\" style=\"vertical-align: -17px;\"><\/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\u5236\u9650\u3092\u5c11\u306a\u304f\u3068\u3082\u7121\u9650\u5927\u307e\u3067\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-c0431a362c02fce505f4567e28f21fa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -\\infty} \\cfrac{x^2+3x+5}{x^4-x-6}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"141\" 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\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5206\u5b50\u306e\u4ee3\u6570\u5f0f\u306e\u6b21\u6570\u306f\u5206\u6bcd\u306e\u5f0f\u306e\u6b21\u6570\u3088\u308a\u5c0f\u3055\u3044\u305f\u3081\u3001\u4e0d\u78ba\u5b9a\u6027 +\u221e\/+\u221e \u306f 0 \u3092\u8fd4\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-405fbcd016c064f414b043abe04fa768_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -\\infty} \\cfrac{x^2+3x+5}{x^4-x-6} = \\cfrac{(-\\infty)^2}{(-\\infty)^4} = \\cfrac{+\\infty}{+\\infty}= \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"316\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 6<\/h3>\n<p>\u30eb\u30fc\u30c8\u3092\u4f7f\u7528\u3057\u3066\u3001\u6b21\u306e\u95a2\u6570\u306e\u4e0d\u5b9a\u6975\u9650\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-159a0cb8cc6c1e4551195c4bb03eacd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\frac{\\sqrt[3]{x^7-4x^3}}{x^2+5x}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"134\" 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\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5206\u5b50\u306e\u5f0f\u306f\u6839\u53f7\u306e\u4e0b\u306b\u3042\u308b\u305f\u3081\u3001\u6b21\u6570\u306f 7\/3 \u3067\u3059\u3002\u4e00\u65b9\u3001\u5206\u6bcd\u306e\u591a\u9805\u5f0f\u306f2\u6b21\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u3057\u3066\u30017\/3&gt;2 \u3067\u3042\u308b\u305f\u3081\u3001\u3053\u306e\u5236\u9650\u306f\u30d7\u30e9\u30b9\u306e\u7121\u9650\u5927\u3092\u4e0e\u3048\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-912b218cb8aa2c4bbc93df147bfb4af6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty}\\frac{\\sqrt[3]{x^7-4x^3}}{x^2+5x}=\\frac{\\sqrt[3]{(+\\infty)^7}}{(+\\infty)^2}=\\frac{+\\infty}{+\\infty}=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"348\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 7<\/h3>\n<p>\u5206\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u6b21\u306e\u95a2\u6570\u306e\u7121\u9650\u5927\u306e\u5236\u9650\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-6ffef148096d3aa64a2eb5d63e00d2f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to +\\infty} \\cfrac{-2x^2}{5-4x}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"101\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u3053\u306e\u6f14\u7fd2\u3067\u306f\u3001\u5206\u5b50\u306e\u6b21\u6570\u304c\u5206\u6bcd\u306e\u6b21\u6570\u3088\u308a\u5927\u304d\u3044\u4e0d\u78ba\u5b9a\u6027\u30de\u30a4\u30ca\u30b9\u7121\u9650\u5927\u3092\u30de\u30a4\u30ca\u30b9\u7121\u9650\u5927\u3067\u5272\u3063\u305f\u5024\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u3088\u3046\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-0b2dfa8a24dd69065fc8ddcf223321d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{-2x^2}{5-4x} = \\cfrac{-2(+\\infty)^2}{-4(+\\infty)} = \\cfrac{-2(+\\infty)}{-\\infty}= \\cfrac{-\\infty}{-\\infty} =\\bm{+\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"431\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 8<\/h3>\n<p>\u6b21\u306e\u95a2\u6570\u306e\u5c11\u306a\u304f\u3068\u3082\u7121\u9650\u5927\u307e\u3067\u306e\u6975\u9650\u3092\u6c42\u3081\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-68566303139abd794f304c979271a058_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -\\infty} \\cfrac{9x}{4-x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"100\" 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\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5206\u6bcd\u591a\u9805\u5f0f\u306f 2 \u6b21\u3067\u3042\u308a\u3001\u5206\u5b50\u591a\u9805\u5f0f\u306f 1 \u6b21\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u4e0d\u78ba\u5b9a\u6027\u306e\u7121\u9650\u5927\u3092\u7121\u9650\u5927\u3067\u5272\u308b\u3068 0 \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-5c5e09be0ae49504103eb4cb5bc2bff7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -\\infty} \\cfrac{9x}{4-x^2} = \\cfrac{9(-\\infty)}{-(-\\infty)^2} = \\cfrac{-\\infty}{-(+\\infty)}=\\cfrac{-\\infty}{-\\infty}= \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"374\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 9<\/h3>\n<p>\u6b21\u306e\u95a2\u6570\u306e\u5c11\u306a\u304f\u3068\u3082\u7121\u9650\u306e\u6975\u9650\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-550b7d336f11ad3346cc238a9f5719db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -\\infty} \\cfrac{-2x^3-3x}{-3x^2+4x-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"163\" 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\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5206\u5b50\u306e\u6b21\u6570\u304c\u5206\u6bcd\u3088\u308a\u5927\u304d\u3044\u305f\u3081\u3001\u4e0d\u5b9a\u5f62 \u221e\/\u221e \u306e\u7d50\u679c\u306f\u7121\u9650\u5927\u306b\u306a\u308a\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u6b63\u3092\u8ca0\u3067\u5272\u308b\u3068\u8ca0\u306b\u306a\u308b\u305f\u3081\u3001\u7121\u9650\u5927\u8a18\u53f7\u306f\u8ca0\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-9820c6575934eac4bea0f71a98db09b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -\\infty} \\cfrac{-2x^3-3x}{-3x^2+4x-1} = \\cfrac{-2(-\\infty)^3}{-3(-\\infty)^2} =\\cfrac{-2(-\\infty)}{-3(+\\infty)}= \\cfrac{+\\infty}{-\\infty}= \\bm{-\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"493\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 10<\/h3>\n<p>\u7121\u9650\u9593\u306e\u7121\u9650\u4e0d\u78ba\u5b9a\u6027\u3092\u4f7f\u7528\u3057\u3066\u6b21\u306e\u6975\u9650\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-5ebe0714beba2eea5d7ab668eb8c75de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to +\\infty}\\cfrac{2^x-4}{-2x^6+x^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"131\" 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\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u6307\u6570\u95a2\u6570\u306f\u591a\u9805\u5f0f\u95a2\u6570\u3088\u308a\u9ad8\u6b21\u3067\u3042\u308b\u305f\u3081\u3001\u6975\u9650\u306f\u7121\u9650\u5927\u306b\u306a\u308a\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u6b63\u3092\u8ca0\u3067\u5272\u308b\u3068\u3001\u7121\u9650\u5927\u306e\u7b26\u53f7\u306f\u8ca0\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-7917d9ddbc8ccb39774511497bdefb5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to +\\infty}\\frac{2^x-4}{-2x^6+x^4}=\\frac{2^{+\\infty}}{-2(+\\infty)^6}=\\frac{+\\infty}{-\\infty}=\\bm{-\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"350\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 11<\/h3>\n<p>\u6b21\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-1aaa5294b445d8033648f190609987c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -\\infty} \\cfrac{x^3-5x}{-x^3-5x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"131\" 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\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u3053\u306e\u554f\u984c\u3067\u306f\u3001\u7121\u9650\u5927\u306e\u4e0d\u78ba\u5b9a\u6027\u7121\u9650\u306f\u30012 \u3064\u306e\u591a\u9805\u5f0f\u306e\u652f\u914d\u7684\u306a\u4fc2\u6570\u3092\u9664\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u89e3\u6c7a\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u305d\u308c\u3089\u304c\u540c\u3058\u6b21\u6570\u3067\u3042\u308b\u305f\u3081\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-f2c768688b8251d2b4313af43af4f746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -\\infty} \\cfrac{x^3-5x}{-x^3-5x^2} = \\cfrac{(-\\infty)^3}{-(-\\infty)^3} = \\cfrac{-\\infty}{-(-\\infty)}= \\cfrac{-\\infty}{+\\infty}=\\cfrac{1}{-1}=\\bm{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"467\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 12<\/h3>\n<p> x \u304c\u7121\u9650\u5927\u306b\u8fd1\u3065\u304f\u3068\u304d\u306e\u6b21\u306e\u95a2\u6570\u306e\u6975\u9650\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-1cce696dca9dec8cf7f859d792996b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{(x+3)^2}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"114\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5206\u5b50\u306e\u672a\u77e5\u6570\u306f\u76f4\u63a5\u4e8c\u4e57\u3055\u308c\u307e\u305b\u3093\u304c\u3001\u6ce8\u76ee\u3059\u3079\u304d\u6052\u7b49\u5f0f\u3092\u89e3\u304f\u3068\u3001\u5206\u5b50\u306e\u6b21\u6570\u304c\u5206\u6bcd\u306e\u6b21\u6570\u3088\u308a\u3082\u5927\u304d\u3044\u3053\u3068\u304c\u660e\u3089\u304b\u306b\u308f\u304b\u308a\u307e\u3059\u3002\u307e\u3060\uff1a <\/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-b93b4ad05b7c3a78f61fe5af296c8055_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{(x+3)^2}{x}=\\lim_{x \\to +\\infty} \\cfrac{x^2+9+6x}{x} = \\cfrac{(+\\infty)^2}{+\\infty} = \\cfrac{+\\infty}{+\\infty} = \\bm{+\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"475\" 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 13<\/h3>\n<p>\u6b21\u306e\u95a2\u6570\u306e\u7121\u9650\u5927\u306e\u6975\u9650\u3092\u7acb\u65b9\u6839\u3067\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-f29e7741e7378d96ef63a5da902d185d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{\\sqrt[3]{8x^3+1}}{-4x}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"125\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5206\u5b50\u306f\u7acb\u65b9\u6839\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u6b21\u6570\u306f 3\/3=1 \u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u5206\u5b50\u306e\u6b21\u6570\u306f\u5206\u6bcd\u306e\u6b21\u6570\u3068\u7b49\u3057\u3044\u305f\u3081\u3001\u7121\u9650\u5927\u9593\u306e\u7121\u9650\u4e0d\u78ba\u5b9a\u6027\u306f\u6b21\u306e\u3088\u3046\u306b\u89e3\u6c7a\u3055\u308c\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-72958d733b74a32ee99322f4adfefb4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{\\sqrt[3]{8x^3+1}}{-4x}= \\cfrac{\\sqrt[3]{8(+\\infty)^3}}{-4(\\infty)}= \\cfrac{+\\infty}{-\\infty}  = \\cfrac{\\sqrt[3]{8}}{-4}=\\cfrac{2}{-4}=\\bm{-}\\mathbf{\\cfrac{1}{2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"444\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 14<\/h3>\n<p> 2 \u3064\u306e\u6839\u53f7\u3092\u4f7f\u7528\u3057\u3066\u3001\u6b21\u306e\u95a2\u6570\u306e\u7121\u9650\u6975\u9650\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-66a62b591cedd9d53e14613fc16bca97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{\\sqrt[3]{6x^7+2x^3}}{\\sqrt{x^5-3x^4+2x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"173\" style=\"vertical-align: -16px;\"><\/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\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5206\u5b50\u306e\u6b21\u6570\u306f 7\/3 = 2.33\u3001\u5206\u6bcd\u306e\u6b21\u6570\u306f 5\/2 = 2.5 \u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5206\u5b50\u306e\u6b21\u6570\u304c\u5206\u6bcd\u306e\u6b21\u6570\u3088\u308a\u5c0f\u3055\u3044\u305f\u3081\u3001\u7121\u9650\u306e\u9593\u306e\u4e0d\u5b9a\u7121\u9650\u6975\u9650\u306f 0 \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-681401701d7d7f3fad1879db26659942_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{\\sqrt[3]{6x^7+2x^3}}{\\sqrt{x^5-3x^4+2x}}=\\cfrac{\\sqrt[3]{6(+\\infty)^7}}{\\sqrt{(+\\infty)^5}}=\\cfrac{+\\infty}{+\\infty}=\\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"376\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 15<\/h3>\n<p>\u6b21\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-fe6ecfeb0afd1ce82003504bdd2222a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{\\sqrt[5]{x^7-2x^5-1}}{4^{x-2}+3x}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"164\" 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\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5206\u5b50\u306e\u6b21\u6570\u306b\u95a2\u4fc2\u306a\u304f\u3001\u5206\u6bcd\u306b\u6307\u6570\u95a2\u6570\u304c\u3042\u308b\u305f\u3081\u3001\u7121\u9650\u5927\u306b\u5bfe\u3059\u308b\u4e0d\u5b9a\u5f62\u5f0f\u306e\u7121\u9650\u5927\u306e\u7d50\u679c\u306f 0 \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-cc9e15968203ed8d39e04b1f2239b9b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} \\cfrac{\\sqrt[5]{x^7-2x^5-1}}{4^{x-2}+3x}=\\cfrac{\\sqrt[5]{(+\\infty)^7}}{4^{+\\infty-2}}=\\cfrac{+\\infty}{+\\infty}=\\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"358\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u7121\u9650\u5927\u9593\u306e\u4e0d\u78ba\u5b9a\u6027\u306e\u7121\u9650\u5927(\u221e\/\u221e)\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u591a\u9805\u5f0f\u3001\u6839\u6570\u3001\u6307\u6570\u95a2\u6570\u306a\u3069\u3001\u3042\u3089\u3086\u308b\u7a2e\u985e\u306e\u95a2\u6570\u3092\u4f7f\u7528\u3057\u305f\u3053\u306e\u4e0d\u6c7a\u5b9a\u306e\u4f8b\u304c\u898b\u3064\u304b\u308a\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u7121\u9650\u9593\u306e\u7121\u9650\u4e0d\u5b9a\u3092\u4e0e\u3048\u308b\u9650\u754c\u3092\u6bb5\u968e\u7684\u306b\u89e3\u6c7a\u3059\u308b\u6f14 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e7%84%a1%e9%99%90%e9%96%93%e3%81%ae%e4%b8%8d%e5%ae%9a%e7%84%a1%e9%99%90-%e2%88%9e-%e2%88%9e\/\"> <span class=\"screen-reader-text\">\u7121\u9650\u9593\u306e\u7121\u9650\u4e0d\u78ba\u5b9a\u6027 (\u221e\/\u221e)<\/span> \u3082\u3063\u3068\u8aad\u3080 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