{"id":22,"date":"2023-09-17T11:07:37","date_gmt":"2023-09-17T11:07:37","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e6%96%9c%e6%b8%90%e8%bf%91%e7%ba%bf\/"},"modified":"2023-09-17T11:07:37","modified_gmt":"2023-09-17T11:07:37","slug":"%e6%96%9c%e6%b8%90%e8%bf%91%e7%ba%bf","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e6%96%9c%e6%b8%90%e8%bf%91%e7%ba%bf\/","title":{"rendered":"\u659c\u6e10\u8fd1\u7ebf"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u89e3\u91ca\u4ec0\u4e48\u662f\u51fd\u6570\u7684\u659c\u6e10\u8fd1\u7ebf\u3002\u60a8\u5c06\u4e86\u89e3\u51fd\u6570\u4f55\u65f6\u5177\u6709\u659c\u6e10\u8fd1\u7ebf\u4ee5\u53ca\u5982\u4f55\u8ba1\u7b97\u5b83\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u770b\u5230\u659c\u6e10\u8fd1\u7ebf\u7684\u793a\u4f8b\uff0c\u5e76\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-asintota-oblicua\"><\/span>\u4ec0\u4e48\u662f\u659c\u6e10\u8fd1\u7ebf\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u51fd\u6570\u7684\u659c\u6e10\u8fd1\u7ebf\u662f\u4e00\u6761\u659c\u7ebf\uff0c\u5176\u56fe\u5f62\u65e0\u9650\u63a5\u8fd1\u4e14\u4e0d\u4f1a\u4e0e\u5176\u76f8\u4ea4\u3002<\/strong>\u56e0\u6b64\uff0c\u6240\u6709\u659c\u6e10\u8fd1\u7ebf\u90fd\u662f\u7b26\u5408\u65b9\u7a0b<em>y=mx+n \u7684<\/em>\u7ebf\u3002<\/p>\n<p>\u659c\u6e10\u8fd1\u7ebf\u7684\u659c\u7387\u548c\u539f\u70b9\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/asymptote-oblique-dune-fonction.webp\" alt=\"\u51fd\u6570\u7684\u659c\u6e10\u8fd1\u7ebf\" class=\"wp-image-1362\" width=\"290\" height=\"328\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-asintota-oblicua-de-una-funcion\"><\/span>\u5982\u4f55\u8ba1\u7b97\u51fd\u6570\u7684\u659c\u6e10\u8fd1\u7ebf<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8981\u8ba1\u7b97\u51fd\u6570\u7684\u659c\u6e10\u8fd1\u7ebf\uff0c\u5fc5\u987b\u6267\u884c\u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;border:\">\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\">\u8ba1\u7b97\u51fd\u6570\u9664\u4ee5 x \u7684\u65e0\u7a77\u5927\u6781\u9650\u3002<\/span><\/li>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u4e0a\u8ff0\u9650\u5236\u5bfc\u81f4\u975e\u96f6\u5b9e\u6570\uff0c\u5219\u610f\u5473\u7740\u8be5\u51fd\u6570\u5177\u6709\u659c\u6e10\u8fd1\u7ebf\u3002\u800c\u4e14\uff0c\u6240\u8ff0\u659c\u6e10\u8fd1\u7ebf\u7684\u659c\u7387\u5c06\u662f\u5728\u6781\u9650\u5904\u83b7\u5f97\u7684\u503c\u3002<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-004f6e72e10d1ba23da76d2fd8ea13f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m = \\lim_{x \\to \\pm\\infty}\\frac{f(x)}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"125\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5269\u4e0b\u7684\u5c31\u662f\u901a\u8fc7\u6c42\u89e3\u4ee5\u4e0b\u6781\u9650\u6765\u8ba1\u7b97\u659c\u6e10\u8fd1\u7ebf\u7684\u622a\u8ddd\uff1a<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9cc74ce0447b0a9148cae947674ad085_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} [f(x)-mx]\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"170\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/ol>\n<p><strong>\u6ce8\u610f\uff1a<\/strong>\u6781\u9650\u5fc5\u987b\u5728\u6b63\u65e0\u7a77\u5927\u548c\u8d1f\u65e0\u7a77\u5927\u5904\u8ba1\u7b97\uff0c\u4f46\u5b83\u4eec\u901a\u5e38\u7ed9\u51fa\u76f8\u540c\u7684\u7ed3\u679c\uff0c\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u6211\u4eec\u901a\u8fc7\u8f93\u5165\u00b1\u65e0\u7a77\u5927\u6765\u7b80\u5316\u3002\u4f46\u5982\u679c\u6b63\u65e0\u7a77\u5927\u548c\u8d1f\u65e0\u7a77\u5927\u7684\u6781\u9650\u4e0d\u540c\uff0c\u5219\u5fc5\u987b\u5206\u522b\u8ba1\u7b97\u5de6\u659c\u6e10\u8fd1\u7ebf\u548c\u53f3\u659c\u6e10\u8fd1\u7ebf\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-asintota-oblicua\"><\/span>\u659c\u6e10\u8fd1\u7ebf\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u91c7\u7528\u4ee5\u4e0b\u6709\u7406\u51fd\u6570\u7684\u659c\u6e10\u8fd1\u7ebf\uff0c\u4ee5\u4fbf\u60a8\u53ef\u4ee5\u770b\u5230\u5982\u4f55\u5b8c\u6210\u6b64\u64cd\u4f5c\u7684\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-b02f6283fd481e890a943badfa2c876f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{x^2+1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"109\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u659c\u6e10\u8fd1\u7ebf\u7684\u7c7b\u578b\u4e3a<\/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-ad313410fc976bc53709807aa8aed8e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=mx+n.\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"95\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u6240\u4ee5\u6211\u4eec\u9996\u5148\u8ba1\u7b97\u76f4\u7ebf\u7684\u659c\u7387<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u53ca\u5176\u76f8\u5e94\u7684\u516c\u5f0f\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-9b50ee5cbc3cf33f7fd42c3fe03a3d71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m = \\lim_{x \\to \\pm\\infty} \\frac{f(x)}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"125\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-870fc158a1aabb54cb5f3b4296381512_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m= \\lim_{x \\to \\pm\\infty} \\cfrac{\\cfrac{x^2+1}{x}}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"141\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u9650\u5236\uff0c\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u5206\u6570\u7684\u6027\u8d28\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-7f313d826cd1a2dd1ef66b1d0a40efb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{\\cfrac{a}{b}}{\\cfrac{c}{d}}=\\cfrac{a\\cdot d}{b\\cdot c}\" title=\"Rendered by QuickLaTeX.com\" height=\"80\" width=\"69\" style=\"vertical-align: -39px;\"><\/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-dfc6b6aa917846535c6c4b6158961988_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m= \\lim_{x \\to \\pm\\infty} \\cfrac{\\cfrac{x^2+1}{x}}{x}=\\lim_{x \\to \\pm\\infty} \\cfrac{x^2+1}{x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"264\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u8ba1\u7b97\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-542fc353481ddc465b7a40f665d3661d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m = \\lim_{x \\to \\pm\\infty} \\cfrac{x^2+1}{x^2} = \\cfrac{+\\infty}{+\\infty} = \\cfrac{1}{1} = \\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"269\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u65e0\u7a77\u5927\u4e4b\u95f4\u7684\u65e0\u7a77\u5927\u4e0d\u786e\u5b9a\u6027\u7684\u7ed3\u679c\u662f\u6700\u9ad8\u6b21 x \u7684\u7cfb\u6570\u76f8\u9664\uff0c\u56e0\u4e3a\u5206\u5b50\u548c\u5206\u6bcd\u5177\u6709\u76f8\u540c\u7684\u9636\u6570\u3002<\/p>\n<p>\u4e0a\u9762\u7684\u6781\u9650\u7ed9\u51fa\u4e86\u4e00\u4e2a\u975e\u96f6\u5b9e\u6570\uff0c\u56e0\u6b64\u8be5\u51fd\u6570\u6709\u4e00\u4e2a\u659c\u6e10\u8fd1\u7ebf\u3002\u6211\u4eec\u73b0\u5728\u5c06\u8ba1\u7b97 y \u8f74\u622a\u8ddd<\/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-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4f7f\u7528\u76f8\u5e94\u7684\u516c\u5f0f\u8ba1\u7b97\u6e10\u8fd1\u7ebf\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-45119c7a74d77a92d7a6cfd5b5c3544f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[f(x)-mx\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"173\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9197669cc0e41aa22224b552b21b31ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[\\cfrac{x^2+1}{x}-1x\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"191\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5c1d\u8bd5\u8ba1\u7b97\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-4d7fa012eace37e82c243012c91f1a5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[\\cfrac{x^2+1}{x}-x\\right] = \\cfrac{+\\infty}{+\\infty} - (+\\infty) = \\bm{+\\infty - \\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"412\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p>\u4f46\u6211\u4eec\u5f97\u5230\u4e0d\u786e\u5b9a\u6027\u65e0\u7a77\u5927\u51cf\u53bb\u65e0\u7a77\u5927\u3002\u56e0\u6b64\uff0c\u6709\u5fc5\u8981\u5c06\u8fd9\u4e9b\u672f\u8bed\u7b80\u5316\u4e3a\u4e00\u4e2a\u516c\u5206\u6bcd\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06 x \u9664\u4ee5\u5206\u6570\u7684\u5206\u6bcd\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-a2355ed9411470b9fd20a50ebbd48726_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n=\\lim_{x \\to \\pm\\infty} \\left[\\cfrac{x^2+1}{x}-\\cfrac{x\\cdot x}{x} \\right] = \\lim_{x \\to \\pm\\infty} \\left[\\cfrac{x^2+1}{x}-\\cfrac{x^2}{x}\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"391\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u8fd9\u4e24\u9879\u5177\u6709\u76f8\u540c\u7684\u5206\u6bcd\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5b83\u4eec\u5206\u7ec4\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-f932ebc8728669c7c6b57e115c444fc7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[\\cfrac{x^2+1}{x}-\\cfrac{x^2}{x} \\right] =  \\lim_{x \\to \\pm\\infty} \\cfrac{x^2+1-x^2}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"358\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5bf9\u5206\u5b50\u8fdb\u884c\u8fd0\u7b97\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-c39259f829c9e99fc88819c6ae266e82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty}  \\cfrac{\\phantom{2}1\\phantom{2}}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"112\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u89e3\u51b3\u4e86\u9650\u5236\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-16a0044416d02e77b05f65f1bb93d4cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty}  \\cfrac{\\phantom{2}1\\phantom{2}}{x}= \\cfrac{1}{\\pm\\infty} = \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"201\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u6240\u4ee5<em>n<\/em> =0\u3002\u56e0\u6b64\uff0c\u659c\u6e10\u8fd1\u7ebf\u662f\u4e00\u4e2a\u7ebf\u6027\u51fd\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-6fbe1cc5f3362ddbd80ed0b29c0bb4ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = mx+n\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"91\" style=\"vertical-align: -4px;\"><\/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-a68ac5c51acd0f68bd022aee64cd9cd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = 1x+0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\"><\/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-4909df7491ef54f0df1e922bc29417f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=x}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u7814\u7a76\u7684\u51fd\u6570\u5982\u4e0b\u56fe\u6240\u793a\u3002\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u8be5\u51fd\u6570\u975e\u5e38\u63a5\u8fd1\u7ebf y=x\uff0c\u4f46\u4ece\u672a\u89e6\u53ca\u5b83\uff0c\u56e0\u4e3a\u5b83\u662f\u659c\u6e10\u8fd1\u7ebf\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/image-1.png\" alt=\"\u659c\u6e10\u8fd1\u7ebf\u7684\u793a\u4f8b\" class=\"wp-image-1374\" width=\"424\" height=\"478\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-asintotas-oblicuas\"><\/span>\u5df2\u89e3\u51b3\u659c\u6e10\u8fd1\u7ebf\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u6c42\u4ee5\u4e0b\u6709\u7406\u51fd\u6570\u7684\u659c\u6e10\u8fd1\u7ebf\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-8ecc70adc78bf259cf6e36c0dcf1bee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\frac{x^2+2x+3}{x+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"150\" 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\">\u659c\u6e10\u8fd1\u7ebf\u7684\u5f62\u5f0f\u4e3a<\/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-8e4adcc4368f6296906b6231bf17a6a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=mx+n\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"91\" style=\"vertical-align: -4px;\"><\/p>\n<p>\uff0c\u56e0\u6b64\u9700\u8981\u8ba1\u7b97\u53c2\u6570<em>m<\/em>\u548c<em>n<\/em> \u3002\u6211\u4eec\u9996\u5148\u901a\u8fc7\u5e94\u7528\u5176\u516c\u5f0f\u6765\u8ba1\u7b97<em>m<\/em> \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-dc38f695cee95c4c60c6e2591345119e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m = \\lim_{x \\to \\pm\\infty} \\frac{f(x)}{x} = \\lim_{x \\to \\pm\\infty} \\cfrac{\\cfrac{x^2+2x+3}{x+1}}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"293\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u901a\u8fc7\u5e94\u7528\u5206\u6570\u7684\u6027\u8d28\u6765\u7b80\u5316\u5206\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-ef59ac0cd51c39c615896543993c12b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m =\\lim_{x \\to \\pm\\infty} \\frac{x^2+2x+3}{(x+1)\\cdot x}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"180\" style=\"vertical-align: -17px;\"><\/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-c51e373fd07a821f8e75d63e38f252dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m =\\lim_{x \\to \\pm\\infty} \\frac{x^2+2x+3}{x^2+x}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"180\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u89e3\u51b3\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-653fa714bca94b5cc4f3ed715d7c1520_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m =\\lim_{x \\to \\pm\\infty} \\frac{x^2+2x+3}{x^2+x}= \\frac{+\\infty}{+\\infty} = \\frac{1}{1} = \\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"308\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5<em>m<\/em> =1\u3002\u73b0\u5728\u8ba9\u6211\u4eec\u5e94\u7528\u516c\u5f0f\u8ba1\u7b97\u659c\u6e10\u8fd1\u7ebf\u7684\u622a\u8ddd\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-e779b5ac239ae56c53427510dbd54dcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[f(x)-mx\\right] = \\lim_{x \\to \\pm\\infty} \\left[ \\frac{x^2+2x+3}{x+1}-1x\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"395\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c1d\u8bd5\u8ba1\u7b97\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-f95f290fbf258d45aa5765008d7aad13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[ \\frac{x^2+2x+3}{x+1}-x\\right]= \\bm{+\\infty - \\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"320\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4f46\u6211\u4eec\u5f97\u5230\u4e86\u65e0\u7a77\u5927\u51cf\u53bb\u65e0\u7a77\u5927\u7684\u4e0d\u5b9a\u5f62\u5f0f\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u5c06\u8fd9\u4e9b\u9879\u7b80\u5316\u4e3a\u4e00\u4e2a\u516c\u5206\u6bcd\uff0c\u7136\u540e\u5c06\u5b83\u4eec\u5206\u7ec4\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-0712d34ed442d9e12ef2490f04df078a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[ \\frac{x^2+2x+3}{x+1}-x\\right] =\\\\[6ex]=\\displaystyle\\lim_{x \\to \\pm\\infty} \\left[ \\frac{x^2+2x+3}{x+1}-\\frac{x \\cdot (x+1)}{x+1} \\right] = \\\\[6ex]=\\displaystyle\\lim_{x \\to \\pm\\infty} \\left[ \\frac{x^2+2x+3}{x+1}-\\frac{x^2+x}{x+1} \\right]=\\\\[6ex]=\\displaystyle\\lim_{x \\to \\pm\\infty} \\frac{x^2+2x+3-(x^2+x)}{x+1}\\\\[6ex]\\displaystyle =\\lim_{x \\to \\pm\\infty} \\frac{x^2+2x+3-x^2-x}{x+1}=\\\\[6ex]=\\displaystyle \\lim_{x \\to \\pm\\infty} \\frac{x+3}{x+1}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"434\" width=\"300\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u89e3\u51b3\u4e86\u9650\u5236\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-ee7e1fdd8e781abed322fed1182ddb15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n =\\lim_{x \\to \\pm\\infty} \\frac{x+3}{x+1} = \\frac{\\infty}{\\infty} = \\frac{1}{1} = \\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"241\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7b80\u800c\u8a00\u4e4b\uff0c\u51fd\u6570\u7684\u659c\u6e10\u8fd1\u7ebf\u4e3a\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-6fbe1cc5f3362ddbd80ed0b29c0bb4ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = mx+n\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"91\" style=\"vertical-align: -4px;\"><\/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-69c0f50795c1f6034c0cd04201f614d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = 1x + 1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\"><\/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-5ffe94db5ae8fa1abc72e6007c2c0586_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y = x + 1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"73\" style=\"vertical-align: -4px;\"><\/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>\u627e\u51fa\u4ee5\u4e0b\u6709\u7406\u51fd\u6570\u7684\u6240\u6709\u659c\u6e10\u8fd1\u7ebf\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-144807b8c72afbd43bb3f97d69cedb35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{2x^2-5}{x+3}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"118\" 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\">\u9996\u5148\uff0c\u6211\u4eec\u4f7f\u7528\u659c\u6e10\u8fd1\u7ebf\u7684\u659c\u7387\u516c\u5f0f\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-bc900ded359235b2293ec151e715daea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m = \\lim_{x \\to \\pm\\infty} \\frac{f(x)}{x} = \\lim_{x \\to \\pm\\infty} \\cfrac{\\cfrac{2x^2-5}{x+3}}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"261\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u901a\u8fc7\u5e94\u7528\u5206\u6570\u7684\u6027\u8d28\u6765\u7b80\u5316\u5206\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-1c5afa9b1ca5f1c73e6b8e64c8fb9420_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m =\\lim_{x \\to \\pm\\infty}\\frac{2x^2-5}{(x+3)\\cdot x}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"168\" style=\"vertical-align: -17px;\"><\/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-03a4b53a445bded103e8de4404620693_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m =\\lim_{x \\to \\pm\\infty}\\frac{2x^2-5}{x^2+3x}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"149\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u786e\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-461c274fc210474eddaf061463e92aaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m =\\lim_{x \\to \\pm\\infty}\\frac{2x^2-5}{x^2+3x}= \\frac{+\\infty}{+\\infty} = \\frac{2}{1} = \\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"278\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6781\u9650\u7ed9\u51fa\u975e\u96f6\u7684\u5b9e\u6570\uff0c\u56e0\u6b64\u5b83\u662f\u4e00\u4e2a\u659c\u6e10\u8fd1\u7ebf\u7684\u6709\u7406\u51fd\u6570\uff0c\u5176\u659c\u7387\u4e3a 2\u3002<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u8ba9\u6211\u4eec\u901a\u8fc7\u5e94\u7528\u76f8\u5e94\u7684\u516c\u5f0f\u6765\u8ba1\u7b97\u622a\u8ddd\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-4a04a1abaebfc5e1781dd7d98399888e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[f(x)-mx\\right] = \\lim_{x \\to \\pm\\infty} \\left[\\frac{2x^2-5}{x+3}-2x\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"364\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c1d\u8bd5\u8ba1\u7b97\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-00f35703d153fe6911328d143588e1cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[\\frac{2x^2-5}{x+3}-2x\\right]= \\bm{+\\infty - \\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"298\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4f46\u6211\u4eec\u5f97\u5230\u4e86\u65e0\u7a77\u5927\u7684\u5dee\u4e0d\u786e\u5b9a\u6027\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u5404\u9879\u7b80\u5316\u4e3a\u516c\u5206\u6bcd\uff0c\u7136\u540e\u8fdb\u884c\u8fd0\u7b97\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-4920e8b21b180c4f2740ce712d9f30d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[\\frac{2x^2-5}{x+3}-2x\\right]=\\\\[6ex]=\\displaystyle\\lim_{x \\to \\pm\\infty} \\left[\\frac{2x^2-5}{x+3}-\\frac{2x\\cdot (x+3)}{x+3} \\right] = \\\\[6ex]=\\displaystyle\\lim_{x \\to \\pm\\infty} \\left[ \\frac{2x^2-5}{x+3}-\\frac{2x^2+6x}{x+3}\\right]=\\\\[6ex]=\\displaystyle\\lim_{x \\to \\pm\\infty}\\frac{2x^2-5-(2x^2+6x)}{x+3}\\\\[6ex]\\displaystyle =\\lim_{x \\to \\pm\\infty}\\frac{2x^2-5-2x^2-6x}{x+3}=\\\\[6ex]=\\displaystyle \\lim_{x \\to \\pm\\infty} \\frac{-6x-5}{x+3}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"434\" width=\"277\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u89e3\u51b3\u4e86\u9650\u5236\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-00b75da44399a44a4e215fd4baccf214_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n =\\lim_{x \\to \\pm\\infty} \\frac{-6x-5}{x+3}= \\frac{\\infty}{\\infty}=\\frac{-6}{1} = \\bm{-6}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"292\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7efc\u4e0a\u6240\u8ff0\uff0c\u5206\u6570\u51fd\u6570\u7684\u659c\u6e10\u8fd1\u7ebf\u4e3a\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-6fbe1cc5f3362ddbd80ed0b29c0bb4ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = mx+n\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"91\" style=\"vertical-align: -4px;\"><\/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-ac6ac25ec7b85209d4d7d855e3d0b501_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=2x-6}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end 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