{"id":366,"date":"2023-07-04T03:00:17","date_gmt":"2023-07-04T03:00:17","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e6%97%a0%e9%99%90-%e2%88%9e-%e2%88%9e-%e4%b9%8b%e9%97%b4%e7%9a%84%e4%b8%8d%e7%a1%ae%e5%ae%9a%e6%80%a7\/"},"modified":"2023-07-04T03:00:17","modified_gmt":"2023-07-04T03:00:17","slug":"%e6%97%a0%e9%99%90-%e2%88%9e-%e2%88%9e-%e4%b9%8b%e9%97%b4%e7%9a%84%e4%b8%8d%e7%a1%ae%e5%ae%9a%e6%80%a7","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e6%97%a0%e9%99%90-%e2%88%9e-%e2%88%9e-%e4%b9%8b%e9%97%b4%e7%9a%84%e4%b8%8d%e7%a1%ae%e5%ae%9a%e6%80%a7\/","title":{"rendered":"\u65e0\u7a77\u5927 (\u65e0\u7a77\u5927\/\u65e0\u7a77\u5927) \u4e4b\u95f4\u7684\u65e0\u9650\u4e0d\u786e\u5b9a\u6027"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u89e3\u91ca\u5982\u4f55\u8ba1\u7b97\u65e0\u7a77\u5927 (\u65e0\u7a77\u5927\/\u65e0\u7a77\u5927) \u4e4b\u95f4\u7684\u4e0d\u786e\u5b9a\u6027\u3002\u60a8\u4f1a\u53d1\u73b0\u8fd9\u79cd\u4e0d\u786e\u5b9a\u6027\u7684\u5404\u79cd\u51fd\u6570\u7684\u4f8b\u5b50\uff1a\u591a\u9879\u5f0f\u3001\u6839\u5f0f\u3001\u6307\u6570\u51fd\u6570\u7b49\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u6781\u9650\u7684\u7ec3\u4e60\u8fdb\u884c\u8bad\u7ec3\uff0c\u8fd9\u4e9b\u6781\u9650\u7ed9\u51fa\u4e86\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u65e0\u9650\u4e0d\u786e\u5b9a\u6027\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-resolver-la-indeterminacion-infinito-entre-infinito\"><\/span>\u5982\u4f55\u89e3\u51b3\u65e0\u7a77\u5927\u4e0e\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u4e0d\u786e\u5b9a\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5f53\u51fd\u6570\u7684\u6781\u9650\u7ed9\u51fa\u65e0\u7a77\u5927\u9664\u4ee5\u65e0\u7a77\u5927\u65f6\uff0c\u5c31\u610f\u5473\u7740\u5b83\u662f\u4e0d\u786e\u5b9a\u6027\uff08\u6216\u4e0d\u786e\u5b9a\u5f62\u5f0f\uff09\u3002\u4e3a\u4e86<strong>\u6c42\u89e3\u7ed9\u51fa\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u4e0d\u786e\u5b9a\u6027\u7684\u51fd\u6570\u7684\u6781\u9650\uff0c<\/strong>\u5fc5\u987b\u5c06\u5206\u5b50\u591a\u9879\u5f0f\u7684\u6b21\u6570\u4e0e\u5206\u6bcd\u591a\u9879\u5f0f\u7684\u6b21\u6570\u8fdb\u884c\u6bd4\u8f83\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\u786e\u5b9a\u6027\u65e0\u7a77\u5927\u9664\u4ee5\u65e0\u7a77\u5927\u7684\u7ed3\u679c\u53d6\u51b3\u4e8e\u5206\u6570\u7684\u5206\u5b50\u6b21\u6570\u548c\u5206\u6bcd\u6b21\u6570\uff1a<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;border:\">\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u5206\u5b50\u591a\u9879\u5f0f\u7684\u6b21\u6570\u5c0f\u4e8e\u5206\u6bcd\u591a\u9879\u5f0f\u7684\u6b21\u6570\uff0c\u5219\u4e0d\u786e\u5b9a\u6027\u7684\u65e0\u7a77\u5927\u9664\u4ee5\u65e0\u7a77<strong><u style=\"text-decoration-color:#FF9B28;\">\u5927\u7b49\u4e8e\u96f6\u3002<\/u><\/strong><\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u5206\u5b50\u591a\u9879\u5f0f\u7684\u6b21\u6570\u7b49\u4e8e\u5206\u6bcd\u591a\u9879\u5f0f\u7684\u6b21\u6570\uff0c\u5219\u65e0\u7a77\u5927\u4e0a\u7684\u65e0\u9650\u4e0d\u786e\u5b9a\u6027\u662f<strong><u style=\"text-decoration-color:#FF9B28;\">\u4e24\u4e2a\u591a\u9879\u5f0f\u7684\u9996\u9879\u7cfb\u6570\u7684\u5546\u3002<\/u><\/strong><\/span><\/li>\n<li><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u5206\u5b50\u591a\u9879\u5f0f\u7684\u6b21\u6570\u5927\u4e8e\u5206\u6bcd\u591a\u9879\u5f0f\u7684\u6b21\u6570\uff0c\u5219\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u4e0d\u786e\u5b9a\u6027\u7ed9\u51fa<strong><u style=\"text-decoration-color:#FF9B28;\">\u6216\u591a\u6216\u5c11\u7684\u65e0\u7a77\u5927<\/u><\/strong>\uff08\u7b26\u53f7\u53d6\u51b3\u4e8e\u4e24\u4e2a\u591a\u9879\u5f0f\u7684\u4e3b\u8981\u9879\uff09\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>\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u65e0\u9650\u4e0d\u786e\u5b9a\u6027\u7684\u4f8b\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8ba9\u6211\u4eec\u901a\u8fc7\u67e5\u770b\u6bcf\u79cd\u60c5\u51b5\u7684\u51e0\u4e2a\u793a\u4f8b\u6765\u770b\u770b\u5982\u4f55\u89e3\u51b3\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u4e0d\u5b9a\u5f62\u5f0f\u65e0\u7a77\u5927\uff1a<\/p>\n<h3 class=\"wp-block-heading\">\u5206\u5b50\u7684\u6b21\u6570\u5c0f\u4e8e\u5206\u6bcd\u7684\u6b21\u6570<\/h3>\n<p>\u6b63\u5982\u6211\u4eec\u5728\u4e0a\u9762\u770b\u5230\u7684\uff0c\u5f53\u5206\u5b50\u591a\u9879\u5f0f\u7684\u6b21\u6570\u5c0f\u4e8e\u5206\u6bcd\u591a\u9879\u5f0f\u7684\u6b21\u6570\u65f6\uff0c\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u65e0\u9650\u4e0d\u786e\u5b9a\u6781\u9650\u603b\u662f\u7ed9\u51fa 0\u3002<\/p>\n<h4 class=\"wp-block-heading\">\u793a\u4f8b1\uff1a<\/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\u7684\u591a\u9879\u5f0f\u662f\u4e8c\u6b21\u591a\u9879\u5f0f\uff0c\u5206\u6bcd\u7684\u591a\u9879\u5f0f\u662f\u4e09\u6b21\u591a\u9879\u5f0f\uff0c\u6240\u4ee5\u6781\u9650\u7684\u89e3\u4e3a0\u3002<\/p>\n<h4 class=\"wp-block-heading\">\u793a\u4f8b2\uff1a<\/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\u7684\u591a\u9879\u5f0f\u51fd\u6570\u662f\u4e00\u6b21\uff0c\u4f46\u5206\u6bcd\u7684\u51fd\u6570\u662f\u56db\u6b21\uff0c\u6240\u4ee5\u8d1f\u65e0\u7a77\u5927\u7684\u6781\u9650\u662f0\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u5206\u5b50\u7684\u6b21\u6570\u7b49\u4e8e\u5206\u6bcd\u7684\u6b21\u6570<\/h3>\n<p>\u5f53\u5206\u5b50\u591a\u9879\u5f0f\u7684\u6b21\u6570\u7b49\u4e8e\u5206\u6bcd\u591a\u9879\u5f0f\u7684\u6b21\u6570\u65f6\uff0c\u901a\u8fc7\u5c06\u4e24\u4e2a\u591a\u9879\u5f0f\u7684\u9996\u9879\u7cfb\u6570\uff08\u8f83\u9ad8\u6b21\u6570\u9879\u7684\u7cfb\u6570\uff09\u76f8\u9664\u6765\u8ba1\u7b97\u4e0d\u5b9a\u6781\u9650\u65e0\u7a77\u5927\u9664\u4ee5\u65e0\u7a77\u5927\u3002<\/p>\n<h4 class=\"wp-block-heading\">\u793a\u4f8b3\uff1a<\/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>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4e24\u4e2a\u591a\u9879\u5f0f\u90fd\u662f\u4e8c\u9636\u591a\u9879\u5f0f\uff0c\u56e0\u6b64\u9700\u8981\u9664\u4ee5\u66f4\u9ad8\u9636\u9879\u7684\u7cfb\u6570\u624d\u80fd\u627e\u5230\u6b63\u65e0\u7a77\u5927\u7684\u6781\u9650\u3002<\/p>\n<h4 class=\"wp-block-heading\">\u793a\u4f8b4\uff1a<\/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>\u867d\u7136\u6781\u9650\u662f\u5f53x\u8d8b\u4e8e\u8d1f\u65e0\u7a77\u5927\u65f6\uff0c\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u65e0\u9650\u4e0d\u786e\u5b9a\u6027\u4ee5\u540c\u6837\u7684\u65b9\u5f0f\u89e3\u51b3\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u5206\u5b50\u7684\u6b21\u6570\u5927\u4e8e\u5206\u6bcd\u7684\u6b21\u6570<\/h3>\n<p>\u5f53\u5206\u5b50\u591a\u9879\u5f0f\u7684\u6b21\u6570\u5927\u4e8e\u5206\u6bcd\u591a\u9879\u5f0f\u7684\u6b21\u6570\u65f6\uff0c\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u65e0\u7a77\u5927\u7684\u4e0d\u5b9a\u5f62\u5f0f\u5c06\u59cb\u7ec8\u7ed9\u51fa\u65e0\u7a77\u5927\uff0c\u5e76\u4e14\u65e0\u7a77\u5927\u7684\u7b26\u53f7\u7531\u4e24\u4e2a\u591a\u9879\u5f0f\u7684\u8f83\u9ad8\u6b21\u6570\u9879\u786e\u5b9a\u3002<\/p>\n<h4 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b5\uff1a<\/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\u7684\u51fd\u6570\u6bd4\u5206\u6bcd\u7684\u51fd\u6570\u5177\u6709\u66f4\u9ad8\u7684\u6b21\u6570\uff0c\u56e0\u6b64\u65e0\u7a77\u5927\u4e0a\u7684\u4e0d\u786e\u5b9a\u6027\u65e0\u7a77\u5927\u7ed9\u51fa\u65e0\u7a77\u5927\u3002\u6b64\u5916\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5206\u5b50\u548c\u5206\u6bcd\u90fd\u4e3a\u6b63\u65e0\u7a77\u5927\uff0c\u56e0\u6b64\u6781\u9650\u7684\u7ed3\u679c\u4e5f\u5fc5\u987b\u4e3a\u6b63\u3002<\/p>\n<h4 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b6\uff1a<\/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>\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u4ece\u5206\u5b50\u83b7\u5f97\u6b63\u65e0\u7a77\u5927\uff0c\u56e0\u4e3a\u4efb\u4f55\u5e73\u65b9\u9879\u90fd\u662f\u6b63\u6570\uff0c\u53e6\u4e00\u65b9\u9762\uff0c\u4ece\u5206\u6bcd\u83b7\u5f97\u8d1f\u65e0\u7a77\u5927\u3002\u56e0\u6b64\uff0c\u6240\u5f97\u6781\u9650\u4e3a\u8d1f\u6570\uff0c\u56e0\u4e3a\u6b63\u6570\u9664\u4ee5\u8d1f\u6570\u7b49\u4e8e\u8d1f\u6570\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-infinito-entre-infinito-con-raices\"><\/span>\u65e0\u7a77\u5927\u4e0e\u6839\u4e4b\u95f4\u7684\u65e0\u9650\u4e0d\u786e\u5b9a\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6211\u4eec\u521a\u521a\u770b\u5230\u4e86\u5f53\u6211\u4eec\u6709\u591a\u9879\u5f0f\u51fd\u6570\u65f6\u5982\u4f55\u8ba1\u7b97\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u65e0\u9650\u4e0d\u786e\u5b9a\u6027\u3002\u4f46\u662f\u2026\u2026\u5982\u679c\u6211\u4eec\u6709\u6839\u7684\u8bdd\uff0c\u65e0\u7a77\u5927\u9664\u4ee5\u65e0\u7a77\u5927\u662f\u591a\u5c11\uff1f<\/p>\n<p><strong>\u65e0\u7406\u51fd\u6570\uff08\u6709\u6839\u51fd\u6570\uff09\u7684<\/strong>\u6b21\u6570\u662f\u4e3b\u9879\u7684\u6b21\u6570\u4e0e\u6839\u5f0f\u6307\u6570\u4e4b\u95f4\u7684\u5546\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>\u56e0\u6b64\uff0c\u5982\u679c<strong>\u6709\u6839\u51fd\u6570\u7684\u6781\u9650\u7ed9\u51fa\u4e86 \u65e0\u7a77\u5927 \u4e4b\u95f4\u7684\u4e0d\u786e\u5b9a\u6027<\/strong>\uff0c\u6211\u4eec\u5fc5\u987b\u5bf9\u5206\u5b50\u548c\u5206\u6bcd\u7684\u6b21\u6570\u5e94\u7528\u4e0a\u9762\u89e3\u91ca\u7684\u76f8\u540c\u89c4\u5219\uff0c\u4f46\u8981\u8003\u8651\u5230\u6709\u6839\u591a\u9879\u5f0f\u7684\u6b21\u6570\u7684\u8ba1\u7b97\u65b9\u5f0f\u4e0d\u540c\u3002<\/p>\n<p>\u8bf7\u770b\u4ee5\u4e0b\u5e26\u6709\u6839\u5f0f\u7684\u51fd\u6570\u7684\u65e0\u7a77\u5927\u6781\u9650\u793a\u4f8b\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-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\u7684\u6b21\u6570\u4e3a 2\uff0c\u5206\u6bcd\u7684\u6b21\u6570\u4e3a 4 (8\/2=4)\uff0c\u56e0\u6b64\u6781\u9650\u4e3a 0\uff0c\u56e0\u4e3a\u5206\u5b50\u7684\u6b21\u6570\u5c0f\u4e8e\u5206\u6bcd\u7684\u6b21\u6570\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u5206\u5b50\u548c\u5206\u6bcd\u7684\u6b21\u6570\u76f8\u7b49\uff0c\u8981\u8ba1\u7b97\u4e0d\u5b9a\u6781\u9650\uff0c\u6211\u4eec\u5fc5\u987b\u7528\u6839\u5f0f\u53d6\u4e3b\u7cfb\u6570\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-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>\u65e0\u7a77\u5927\u4e0e\u6307\u6570\u51fd\u6570\u4e4b\u95f4\u7684\u65e0\u9650\u4e0d\u786e\u5b9a\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u53ea\u9700\u8981\u7814\u7a76\u65e0\u7a77\u5927\u7684\u4e0d\u786e\u5b9a\u5546\u7684\u4e00\u4e2a\u4f8b\u5b50\uff1a\u65e0\u7a77\u5927\u548c\u6307\u6570\u51fd\u6570\u4e4b\u95f4\u7684\u65e0\u7a77\u4e0d\u786e\u5b9a\u5546\u662f\u591a\u5c11\u3002<\/p>\n<p>\u6307\u6570\u51fd\u6570\u7684\u589e\u957f\u8fdc\u5927\u4e8e\u591a\u9879\u5f0f\u51fd\u6570\u7684\u589e\u957f\uff0c<strong>\u56e0\u6b64\u6211\u4eec\u5fc5\u987b\u8003\u8651\u6307\u6570\u51fd\u6570\u7684\u6b21\u6570\u5927\u4e8e\u591a\u9879\u5f0f\u51fd\u6570\u7684\u6b21\u6570\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>\u56e0\u6b64\uff0c\u5982\u679c\u65e0\u7a77\u5927\u7684\u4e0d\u786e\u5b9a\u6027\u9664\u4ee5\u65e0\u7a77\u5927\u662f\u7531\u6307\u6570\u51fd\u6570\u7684\u6781\u9650\u5f97\u51fa\u7684\uff0c\u5219\u5e94\u7528\u5bf9\u5206\u5b50\u548c\u5206\u6bcd\u7684\u6b21\u6570\u89e3\u91ca\u7684\u76f8\u540c\u89c4\u5219\u5c31\u8db3\u591f\u4e86\uff0c\u4f46\u8981\u8003\u8651\u5230\u6307\u6570\u51fd\u6570\u7684\u9636\u6570\u6bd4\u591a\u9879\u5f0f\u9ad8\u3002 \u3002<\/p>\n<p>\u6b64\u5916\uff0c\u5982\u679c\u9664\u6cd5\u7684\u5206\u5b50\u548c\u5206\u6bcd\u4e2d\u6709\u6307\u6570\u51fd\u6570\uff0c\u5219\u5e95\u6570\u8d8a\u5927\u7684\u6307\u6570\u51fd\u6570\u7684\u9636\u6570\u8d8a\u9ad8\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>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5206\u6bcd\u7531\u6307\u6570\u51fd\u6570\u5f62\u6210\uff0c\u56e0\u6b64\u5b83\u7684\u9636\u6570\u6bd4\u5206\u5b50\u9ad8\u3002\u56e0\u6b64\uff0c\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u4e0d\u786e\u5b9a\u5f62\u5f0f\u65e0\u7a77\u5927\u6d88\u5931\u4e86\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-indeterminacion-infinito-entre-infinito\"><\/span>\u89e3\u51b3\u4e86\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u65e0\u9650\u4e0d\u786e\u5b9a\u6027\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u6709\u7406\u51fd\u6570\u7684\u6781\u9650\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-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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5728\u8ba1\u7b97\u6781\u9650\u65f6\uff0c\u6211\u4eec\u5f97\u5230\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u65e0\u9650\u4e0d\u786e\u5b9a\u6027\uff0c\u4f46\u7531\u4e8e\u5206\u5b50\u7684\u6b21\u6570\u5c0f\u4e8e\u5206\u6bcd\u7684\u6b21\u6570\uff0c\u56e0\u6b64\u4e0d\u786e\u5b9a\u6781\u9650\u7b49\u4e8e\u96f6\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\">\u7ec3\u4e602<\/h3>\n<p>\u6c42\u89e3\u4e0b\u5217\u4e0d\u5b9a\u6781\u9650\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-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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5f53\u5c1d\u8bd5\u8ba1\u7b97\u6781\u9650\u65f6\uff0c\u4f1a\u5f97\u5230\u4e0d\u786e\u5b9a\u6027 \u221e\/\u221e\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5206\u5b50\u591a\u9879\u5f0f\u7684\u6b21\u6570\u5927\u4e8e\u5206\u6bcd\u591a\u9879\u5f0f\u7684\u6b21\u6570\uff0c\u56e0\u6b64\u4e0d\u786e\u5b9a\u6781\u9650\u7b49\u4e8e\u52a0\u4e0a\u65e0\u7a77\u5927\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\">\u7ec3\u4e603<\/h3>\n<p>\u6c42\u89e3\u4ee5\u4e0b\u65e0\u7a77\u8fdc\u6781\u9650\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-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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8be5\u6781\u9650\u7ed9\u51fa\u4e86\u6b63\u65e0\u7a77\u5927\u4e0e\u8d1f\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u4e0d\u786e\u5b9a\u6027\u3002\u5206\u5b50\u7684\u6b21\u6570\u5927\u4e8e\u5206\u6bcd\u7684\u6b21\u6570\uff0c\u56e0\u6b64\u4e0d\u5b9a\u6781\u9650\u7b49\u4e8e\u52a0\u4e0a\u65e0\u7a77\u5927\u3002\u7136\u800c\uff0c\u7531\u4e8e\u9664\u6cd5\u662f\u8d1f\u65e0\u7a77\u5927\u9664\u4ee5\u6b63\u65e0\u7a77\u5927\uff0c\u56e0\u6b64\u7ed3\u679c\u662f\u8d1f\u65e0\u7a77\u5927\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\">\u7ec3\u4e604<\/h3>\n<p>\u6c42\u89e3\u4e0b\u5217\u4e0d\u5b9a\u6781\u9650\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-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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u65e0\u7a77\u5927\u4e0a\u7684\u65e0\u9650\u4e0d\u5b9a\u5f62\u5f0f\u662f\u7531\u4e24\u4e2a\u540c\u6b21\u591a\u9879\u5f0f\u7684\u5546\u5f97\u5230\u7684\uff0c\u56e0\u6b64\uff0c\u4e0d\u5b9a\u6781\u9650\u7684\u7ed3\u679c\u662f\u5b83\u4eec\u7684\u4e3b\u8981\u7cfb\u6570\u7684\u9664\u6cd5\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-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\">\u7ec3\u4e605<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u81f3\u5c11\u5230\u65e0\u7a77\u5927\u7684\u6781\u9650\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-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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5206\u5b50\u7684\u4ee3\u6570\u8868\u8fbe\u5f0f\u7684\u6b21\u6570\u5c0f\u4e8e\u5206\u6bcd\u7684\u4ee3\u6570\u8868\u8fbe\u5f0f\u7684\u6b21\u6570\uff0c\u56e0\u6b64\u4e0d\u786e\u5b9a\u6027 +\u221e\/+\u221e \u7ed9\u51fa 0\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-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\">\u7ec3\u4e606<\/h3>\n<p>\u6c42\u89e3\u4ee5\u4e0b\u6709\u6839\u51fd\u6570\u7684\u4e0d\u5b9a\u6781\u9650\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-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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5206\u5b50\u7684\u8868\u8fbe\u5f0f\u4f4d\u4e8e\u6839\u5f0f\u4e0b\u65b9\uff0c\u56e0\u6b64\u5176\u6b21\u6570\u4e3a 7\/3\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5206\u6bcd\u4e2d\u7684\u591a\u9879\u5f0f\u662f\u4e8c\u6b21\u7684\u3002\u7531\u4e8e 7\/3&gt;2\uff0c\u6781\u9650\u7ed9\u51fa\u6b63\u65e0\u7a77\u5927\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-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\">\u7ec3\u4e607<\/h3>\n<p>\u786e\u5b9a\u4ee5\u4e0b\u5e26\u5206\u6570\u51fd\u6570\u7684\u65e0\u7a77\u5927\u6781\u9650\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-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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5728\u672c\u7ec3\u4e60\u4e2d\uff0c\u5206\u5b50\u6b21\u6570\u5927\u4e8e\u5206\u6bcd\u6b21\u6570\u65f6\uff0c\u53ef\u5f97\u5230\u4e0d\u786e\u5b9a\u6027\u8d1f\u65e0\u7a77\u5927\u9664\u4ee5\u8d1f\u65e0\u7a77\u5927\uff0c\u56e0\u6b64\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-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\">\u7ec3\u4e608<\/h3>\n<p>\u6c42\u4e0b\u5217\u51fd\u6570\u7684\u81f3\u5c11\u65e0\u7a77\u5927\u6781\u9650\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-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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5206\u6bcd\u591a\u9879\u5f0f\u662f\u4e8c\u6b21\u7684\uff0c\u800c\u5206\u5b50\u591a\u9879\u5f0f\u662f\u7ebf\u6027\u7684\u3002\u56e0\u6b64\uff0c\u4e0d\u786e\u5b9a\u6027\u7684\u65e0\u7a77\u5927\u9664\u4ee5\u65e0\u7a77\u5927\u5f97\u5230 0\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\">\u7ec3\u4e609<\/h3>\n<p>\u6c42\u89e3\u4ee5\u4e0b\u51fd\u6570\u7684\u81f3\u5c11\u65e0\u9650\u6781\u9650\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-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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5206\u5b50\u7684\u6b21\u6570\u5927\u4e8e\u5206\u6bcd\uff0c\u56e0\u6b64\u4e0d\u5b9a\u5f62\u5f0f \u221e\/\u221e \u7684\u7ed3\u679c\u5c06\u662f\u65e0\u7a77\u5927\u3002\u6b64\u5916\uff0c\u65e0\u7a77\u5927\u7b26\u53f7\u5c06\u4e3a\u8d1f\u6570\uff0c\u56e0\u4e3a\u6b63\u6570\u9664\u4ee5\u8d1f\u6570\u5f97\u5230\u8d1f\u6570\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-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\">\u7ec3\u4e6010<\/h3>\n<p>\u6c42\u89e3\u4ee5\u4e0b\u5177\u6709\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u65e0\u9650\u4e0d\u786e\u5b9a\u6027\u7684\u6781\u9650\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-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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u6307\u6570\u51fd\u6570\u7684\u9636\u6570\u9ad8\u4e8e\u591a\u9879\u5f0f\u51fd\u6570\uff0c\u56e0\u6b64\u6781\u9650\u5c06\u4e3a\u65e0\u7a77\u5927\u3002\u4f46\u662f\uff0c\u5c06\u6b63\u6570\u9664\u4ee5\u8d1f\u6570\uff0c\u65e0\u7a77\u5927\u7b26\u53f7\u5c06\u4e3a\u8d1f\u6570\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-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\">\u7ec3\u4e6011<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u6781\u9650\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-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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u65e0\u7a77\u5927\u4e0a\u7684\u4e0d\u786e\u5b9a\u6027\u901a\u8fc7\u9664\u4e24\u4e2a\u591a\u9879\u5f0f\u7684\u4e3b\u7cfb\u6570\u6765\u89e3\u51b3\uff0c\u56e0\u4e3a\u5b83\u4eec\u5177\u6709\u76f8\u540c\u7684\u6b21\u6570\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-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\">\u7ec3\u4e6012<\/h3>\n<p>\u5f53 x \u63a5\u8fd1\u65e0\u7a77\u5927\u65f6\uff0c\u6c42\u89e3\u4ee5\u4e0b\u51fd\u6570\u7684\u6781\u9650\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-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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u867d\u7136\u5206\u5b50\u4e2d\u7684\u672a\u77e5\u6570\u4e0d\u662f\u76f4\u63a5\u5e73\u65b9\u7684\uff0c\u4f46\u5728\u6c42\u89e3\u663e\u7740\u6052\u7b49\u5f0f\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u6e05\u695a\u5730\u770b\u5230\u5206\u5b50\u7684\u6b21\u6570\u5927\u4e8e\u5206\u6bcd\u7684\u6b21\u6570\u3002\u7136\u800c\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\">\u7ec3\u4e6013<\/h3>\n<p>\u4f7f\u7528\u7acb\u65b9\u6839\u8ba1\u7b97\u4ee5\u4e0b\u51fd\u6570\u7684\u65e0\u7a77\u5927\u6781\u9650\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-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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5206\u5b50\u7531\u7acb\u65b9\u6839\u7ec4\u6210\uff0c\u56e0\u6b64\u5176\u6b21\u6570\u4e3a3\/3=1\u3002\u90a3\u4e48\uff0c\u5206\u5b50\u7684\u6b21\u6570\u7b49\u4e8e\u5206\u6bcd\u7684\u6b21\u6570\uff0c\u56e0\u6b64\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u65e0\u9650\u4e0d\u786e\u5b9a\u6027\u53ef\u4ee5\u5982\u4e0b\u89e3\u51b3\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-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\">\u7ec3\u4e6014<\/h3>\n<p>\u6c42\u89e3\u4ee5\u4e0b\u5e26\u6709\u4e24\u4e2a\u6839\u5f0f\u7684\u51fd\u6570\u7684\u65e0\u7a77\u5927\u6781\u9650\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-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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5206\u5b50\u7684\u6b21\u6570\u4e3a 7\/3 = 2.33\uff0c\u5206\u6bcd\u7684\u6b21\u6570\u4e3a 5\/2 = 2.5\u3002\u56e0\u6b64\uff0c\u7531\u4e8e\u5206\u5b50\u7684\u6b21\u6570\u5c0f\u4e8e\u5206\u6bcd\u7684\u6b21\u6570\uff0c\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u4e0d\u786e\u5b9a\u65e0\u9650\u6781\u9650\u4e3a 0\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-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\">\u7ec3\u4e6015<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u6781\u9650\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-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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u65e0\u8bba\u5206\u5b50\u7684\u6b21\u6570\u5982\u4f55\uff0c\u7531\u4e8e\u5206\u6bcd\u4e2d\u6709\u4e00\u4e2a\u6307\u6570\u51fd\u6570\uff0c\u56e0\u6b64\u65e0\u7a77\u5927\u7684\u4e0d\u5b9a\u5f62\u5f0f\u7684\u7ed3\u679c\u662f 0\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-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>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u89e3\u91ca\u5982\u4f55\u8ba1\u7b97\u65e0\u7a77\u5927 (\u65e0\u7a77\u5927\/\u65e0\u7a77\u5927) \u4e4b\u95f4\u7684\u4e0d\u786e\u5b9a\u6027\u3002\u60a8\u4f1a\u53d1\u73b0\u8fd9\u79cd\u4e0d\u786e\u5b9a\u6027\u7684\u5404\u79cd\u51fd\u6570\u7684\u4f8b\u5b50\uff1a &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e6%97%a0%e9%99%90-%e2%88%9e-%e2%88%9e-%e4%b9%8b%e9%97%b4%e7%9a%84%e4%b8%8d%e7%a1%ae%e5%ae%9a%e6%80%a7\/\"> <span class=\"screen-reader-text\">\u65e0\u7a77\u5927 (\u65e0\u7a77\u5927\/\u65e0\u7a77\u5927) \u4e4b\u95f4\u7684\u65e0\u9650\u4e0d\u786e\u5b9a\u6027<\/span> \u67e5\u770b\u5168\u6587 &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-366","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized 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