{"id":26,"date":"2023-09-17T11:04:43","date_gmt":"2023-09-17T11:04:43","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e5%9d%87%e5%92%8c%e7%9e%ac%e6%97%b6%e5%8f%98%e5%8c%96%e7%8e%87\/"},"modified":"2023-09-17T11:04:43","modified_gmt":"2023-09-17T11:04:43","slug":"%e5%b9%b3%e5%9d%87%e5%92%8c%e7%9e%ac%e6%97%b6%e5%8f%98%e5%8c%96%e7%8e%87","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e5%9d%87%e5%92%8c%e7%9e%ac%e6%97%b6%e5%8f%98%e5%8c%96%e7%8e%87\/","title":{"rendered":"\u5e73\u5747\u548c\u77ac\u65f6\u53d8\u5316\u7387"},"content":{"rendered":"<p>\u8fd9\u91cc\u6211\u4eec\u89e3\u91ca\u4ec0\u4e48\u662f\u53d8\u5316\u7387\u3001\u5e73\u5747\u53d8\u5316\u7387\u548c\u77ac\u65f6\u53d8\u5316\u7387\u3002\u60a8\u5c06\u80fd\u591f\u770b\u5230\u51e0\u4e2a\u6709\u5173\u5982\u4f55\u8ba1\u7b97\u53d8\u5316\u7387\u7684\u793a\u4f8b\uff0c\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u53d8\u5316\u7387\u5206\u6b65\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-tasa-de-variacion\"><\/span>\u53d8\u5316\u7387\u662f\u591a\u5c11\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5728\u6570\u5b66\u4e2d\uff0c\u51fd\u6570\u7684\u53d8\u5316\u7387\uff08TV\uff09\u662f\u51fd\u6570\u5728\u4e24\u4e2a\u4e0d\u540c\u70b9\u5904\u7684\u503c\u4e4b\u5dee\u3002<\/strong>\u56e0\u6b64\uff0c\u8981\u8ba1\u7b97\u4e24\u70b9\u4e4b\u95f4\u7684\u53d8\u5316\u7387\uff0c\u5fc5\u987b\u5c06\u8fd9\u4e24\u70b9\u5904\u7684\u51fd\u6570\u503c\u76f8\u51cf\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-c33fec724dd0a5bf45bfec5a911f5bcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TV}[a,b]=f(b)-f(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4f8b\u5982\uff0c\u5982\u679c\u51fd\u6570\u7684\u4e24\u4e2a\u56fe\u50cf\u5206\u522b\u4e3a f(2)=1 \u548c f(5)=7\uff0c\u5219\u5b83\u4eec\u7684\u53d8\u5316\u7387\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-8696c8ddc5db28bea4a9b14bc6dc0b9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TV}[2,5]=f(5)-f(2)=7-1=6\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"269\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u521a\u521a\u770b\u5230\u4e86\u53d8\u5316\u7387\u7684\u6570\u5b66\u542b\u4e49\uff0c\u4f46\u5728\u7ecf\u6d4e\u5b66\u4e2d\uff0c\u53d8\u5316\u7387\u7684\u6982\u5ff5\u542b\u4e49\u5982\u4e0b\uff1a<\/p>\n<p>\u5728\u7ecf\u6d4e\u5b66\u4e2d\uff0c\u4e24\u4e2a\u6570\u503c\u4e4b\u95f4\u7684\u53d8\u5316\u7387\u662f\u7528\u767e\u5206\u6bd4\u8868\u793a\u7684\u5b83\u4eec\u4e4b\u95f4\u7684\u5dee\u503c\uff0c\u5373\u4e00\u4e2a\u53d8\u91cf\u5728\u4e0d\u540c\u65f6\u671f\u4e4b\u95f4\u7684\u53d8\u5316\u7387\u5c31\u662f\u5b83\u7684\u76f8\u5bf9\u53d8\u5316\u3002\u56e0\u6b64\uff0c\u8981\u8ba1\u7b97\u53d8\u5316\u7387\uff0c\u9700\u8981\u5c06\u4e24\u4e2a\u4e0d\u540c\u5468\u671f\u7684\u503c\u76f8\u51cf\uff0c\u5e76\u5c06\u5f97\u5230\u7684\u7ed3\u679c\u9664\u4ee5\u521d\u59cb\u5468\u671f\u7684\u503c\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-3a6392a6712643e5eeddbf7226523e42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TV}[t,t+n]=\\cfrac{Y_{t+n}-Y_t}{Y_t}\\cdot 100\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"227\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p>\u4f8b\u5982\uff0c\u5982\u679c\u67d0\u4e9b\u80a1\u7968\u7684\u4ef7\u503c\u5728\u4e00\u4e2a\u6708\u5185\u4ece 35 \u6b27\u5143\u589e\u52a0\u5230 50 \u6b27\u5143\uff0c\u5219\u5176\u53d8\u52a8\u7387\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-17a18b6b77c1e1b21cad5d1ffab56aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TV}[t,t+1]=\\cfrac{50-35}{35}\\cdot 100=42,86 \\ \\%\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"296\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u8003\u8651\u5230\u53d8\u5316\u7387\u7684\u4e24\u79cd\u53ef\u80fd\u542b\u4e49\uff0c\u5728\u672c\u6587\u4e2d\u6211\u4eec\u5c06\u91cd\u70b9\u4e86\u89e3\u53d8\u5316\u7387\u7684\u6570\u5b66\u5b9a\u4e49\u3002\u53ef\u4ee5\u533a\u5206\u4e24\u79cd\u7c7b\u578b\u7684\u53d8\u5316\u7387\uff1a\u5e73\u5747\u53d8\u5316\u7387\u548c\u77ac\u65f6\u53d8\u5316\u7387\u3002\u4e0b\u9762\u662f\u6bcf\u79cd\u7c7b\u578b\u7684\u89e3\u91ca\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tasa-de-variacion-media\"><\/span> \u5e73\u5747\u53d8\u5316\u7387<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u51fd\u6570\u5728\u67d0\u4e2a\u533a\u95f4\u5185\u7684\u5e73\u5747\u53d8\u5316\u7387 (TVM) \u662f\u6307\u51fd\u6570\u81ea\u53d8\u91cf\u6bcf\u589e\u52a0\u4e00\u4e2a\u5355\u4f4d\u800c\u589e\u52a0\uff08\u6216\u51cf\u5c11\uff09\u7684\u5355\u4f4d\u6570\u3002<\/strong>\u56e0\u6b64\uff0c\u51fd\u6570\u7684\u5e73\u5747\u53d8\u5316\u7387\u662f\u901a\u8fc7\u5c06\u51fd\u6570\u5728\u67d0\u4e2a\u533a\u95f4\u5185\u7684\u589e\u957f\u9664\u4ee5\u8be5\u540c\u4e00\u533a\u95f4\u7684\u5e45\u5ea6\u6765\u8ba1\u7b97\u7684\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-a08373207642a78dec20dd28a9dafc4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVM}[a,b]=\\cfrac{f(b)-f(a)}{b-a}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"191\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u8ba9\u60a8\u4e86\u89e3\u5e73\u5747\u53d8\u5316\u7387\u662f\u5982\u4f55\u8ba1\u7b97\u7684\uff0c\u6211\u4eec\u5728\u4e0b\u9762\u9010\u6b65\u89e3\u51b3\u4e86\u4e00\u4e2a\u793a\u4f8b\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-de-la-tasa-de-variacion-media-de-una-funcion\"><\/span>\u8ba1\u7b97\u51fd\u6570\u5e73\u5747\u53d8\u5316\u7387\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>\u8ba1\u7b97\u4ee5\u4e0b\u51fd\u6570\u5728\u533a\u95f4[2.5]\u5185\u7684\u5e73\u5747\u53d8\u5316\u7387\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e583988ce73cdf54a12306a64c97cc42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) = x^2-1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u8ba1\u7b97\u51fd\u6570\u5728 x=2 \u548c x=5 \u5904\u7684\u503c\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-57a8756268ece6ee3543392da3aa5ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(5)= 5^2-1=25-1=24\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"217\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7163ad8fbbfd700e474e6d40164c8cb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(2)=2^2-1=4-1=3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"200\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u7136\u540e\u6211\u4eec\u7b80\u5355\u5730\u5e94\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u51fd\u6570\u5728\u533a\u95f4\u5185\u7684\u5e73\u5747\u53d8\u5316\u7387\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-aca6688a94500231cb464ce5ca91685c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVM} [a,b] = \\cfrac{f(b)-f(a)}{b-a}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"191\" 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-dba3fad93a4b7e04a5d6f1517eb6dc1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVM} [2,5]=\\cfrac{f(5)-f(2)}{5-2} = \\cfrac{24 - 3}{5-2} = \\cfrac{21}{3} = \\bm{7}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"341\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u7531\u4e8eTVM[2,5]\u7684\u7ed3\u679c\u4e3a\u6b63\uff0c\u8fd9\u610f\u5473\u7740\u51fd\u6570\u5728\u533a\u95f4[2,5]\u5185\u589e\u957f\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u7ed3\u679c\u4e3a\u8d1f\uff0c\u5219\u610f\u5473\u7740\u51fd\u6570\u5728\u6b64\u533a\u95f4\u5185\u4e0b\u964d\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"interpretacion-geometrica-de-la-tasa-de-variacion-media\"><\/span>\u5e73\u5747\u53d8\u5316\u7387\u7684\u51e0\u4f55\u89e3\u91ca<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u5728\u51e0\u4f55\u4e0a\uff0c\u51fd\u6570\u5728\u533a\u95f4\u5185\u7684\u5e73\u5747\u53d8\u5316\u7387\u8868\u793a\u8fde\u63a5\u533a\u95f4\u6781\u503c\u70b9\u7684\u76f4\u7ebf\u7684\u659c\u7387\u3002 <\/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\/taux-de-variation-moyen.webp\" alt=\"\u5e73\u5747\u53d8\u5316\u7387\" class=\"wp-image-1678\" width=\"337\" height=\"378\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tasa-de-variacion-instantanea\"><\/span>\u77ac\u65f6\u53d8\u5316\u7387<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u51fd\u6570\u5728\u67d0\u4e00\u70b9\u7684\u77ac\u65f6\u53d8\u5316\u7387 (TVI) \u662f\u51fd\u6570\u5728\u4e00\u6bb5\u65f6\u95f4\u5185\u76f8\u5bf9\u589e\u52a0\u7684\u65e0\u7a77\u5c0f\u6781\u9650\u3002<\/strong>\u56e0\u6b64\uff0c\u901a\u8fc7<em>\u4f7f<\/em><em>h<\/em>\u8d8b\u4e8e\u96f6\u6765\u6c42\u89e3<em>f(a+h)-f(a)<\/em>\u7684\u5546\u7684\u6781\u9650\u6765\u8ba1\u7b97\u77ac\u65f6\u53d8\u5316\u7387\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-605387fef74bd8fe7f7e8a3e75686a7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{TVI}(a)=\\lim_{h \\to 0}\\frac{f(a+h)-f(a)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"235\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u77ac\u65f6\u53d8\u5316\u7387\u7684\u503c\u53ef\u4ee5\u662f\u6b63\u6570\u3001\u8d1f\u6570\u6216\u96f6\uff0c\u8868\u793a\u8be5\u70b9\u7684\u51fd\u6570\u5728\u8be5\u70b9\u5206\u522b\u662f\u589e\u52a0\u3001\u51cf\u5c11\u6216\u4fdd\u6301\u4e0d\u53d8\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-de-la-tasa-de-variacion-instantanea-de-una-funcion\"><\/span>\u8ba1\u7b97\u51fd\u6570\u77ac\u65f6\u53d8\u5316\u7387\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>\u8ba1\u7b97\u4ee5\u4e0b\u51fd\u6570\u5728 x=2 \u70b9\u5904\u7684\u77ac\u65f6\u53d8\u5316\u7387\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a0f6973d1b2b1b370cb20764d5a954a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) = x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u8ba1\u7b97\u77ac\u65f6\u53d8\u5316\u7387\uff0c\u6211\u4eec\u9700\u8981\u5e94\u7528\u4ee5\u4e0b\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-ef687e3c0bab81c2a8eaa578fcc41b9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVI} (a) = \\lim\\limits_{h \\to 0} \\cfrac{f(a+h)-f(a)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"235\" style=\"vertical-align: -13px;\"><\/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-fd6499ec6074ceea794309155c7d788d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVI} (2) = \\lim\\limits_{h \\to 0} \\cfrac{f(2+h)-f(2)}{h} =  \\lim\\limits_{h \\to 0} \\cfrac{(2+h)^2-2^2}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"390\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u89e3\u6790\u663e\u7740\u7684\u8eab\u4efd\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-21ea1067eb0c47009dd7f9c214a16e4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{h \\to 0}  \\cfrac{2^2+h^2+2\\cdot 2 \\cdot h -2^2}{h} = \\lim\\limits_{h \\to 0}  \\cfrac{4+h^2+4h -4}{h} = \\lim\\limits_{h \\to 0}  \\cfrac{h^2+4h}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"496\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#FF9B28;\">\u27a4<\/span>\u5982\u679c\u60a8\u4e0d\u518d\u8bb0\u5f97<u style=\"text-decoration-color:#FF9B28;\">\u91cd\u8981\u6052\u7b49\u5f0f\u7684\u516c\u5f0f<\/u>\uff0c\u60a8\u53ef\u4ee5\u5728\u6211\u4eec\u4e13\u95e8\u7814\u7a76\u591a\u9879\u5f0f\u7684\u7f51\u7ad9\u4e0a\u627e\u5230\u6240\u6709\u516c\u5f0f\uff1a <u style=\"text-decoration-color:#FF9B28;\">www.polinomios.org<\/u><\/p>\n<p>\u73b0\u5728\u8ba9\u6211\u4eec\u5c1d\u8bd5\u89e3\u51b3\u8fd9\u4e2a\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-b380a5546aa95d74c4da1a81e0e4665b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{h \\to 0}  \\cfrac{h^2+4h}{h} = \\cfrac{0^2+4\\cdot 0}{0} =\\cfrac{0}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"221\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u4f46\u6211\u4eec\u53d1\u73b0\u96f6\u4e4b\u95f4\u7684\u4e0d\u786e\u5b9a\u6027\u4e3a\u96f6\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-ae32dac146777b5395b505ebf658af5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{h \\to 0}  \\cfrac{h^2+4h}{h}= \\lim\\limits_{h \\to 0} \\cfrac{\\cancel{h}(h+4)}{\\cancel{h}} = \\lim\\limits_{h \\to 0} (h+4)\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"320\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u96f6\u4e4b\u95f4-\u96f6-0-0-\u4e0d\u786e\u5b9a\/\">\u5982\u4f55\u6c42\u89e3\u96f6\u4e4b\u95f4\u5177\u6709\u96f6\u4e0d\u786e\u5b9a\u6027\u7684\u6781\u9650<\/a><\/span><\/p>\n<p>\u6700\u540e\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-3b124f5a6537497e232294814f1d49b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{h \\to 0} (h+4) = 0 +4 = \\bm{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"179\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\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-9504f8df3dcdd1c6954399b5a6aa0ef4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathbf{TVI} \\bm{(2) = 4}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u7531\u4e8e TVI(2) \u7684\u7ed3\u679c\u4e3a\u6b63\uff0c\u8fd9\u610f\u5473\u7740\u51fd\u6570\u5728 x=2 \u65f6\u589e\u52a0\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u7ed3\u679c\u4e3a\u8d1f\uff0c\u5219\u610f\u5473\u7740\u8be5\u51fd\u6570\u5728\u6b64\u9636\u6bb5\u6b63\u5728\u4e0b\u964d\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"interpretacion-geometrica-de-la-tasa-de-variacion-instantanea\"><\/span>\u77ac\u65f6\u53d8\u5316\u7387\u7684\u51e0\u4f55\u89e3\u91ca<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u4ece\u51e0\u4f55\u89d2\u5ea6\u6765\u770b\uff0c\u51fd\u6570\u5728\u67d0\u4e00\u70b9\u7684\u77ac\u65f6\u53d8\u5316\u7387\u8868\u793a\u8be5\u51fd\u6570\u5728\u8be5\u70b9\u7684\u5207\u7ebf\u7684\u659c\u7387\u3002 <\/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\/taux-de-changement-instantane.webp\" alt=\"\u77ac\u65f6\u53d8\u5316\u7387\" class=\"wp-image-1682\" width=\"336\" height=\"355\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u5982\u679c\u4ed4\u7ec6\u770b\u7684\u8bdd\uff0c\u77ac\u65f6\u53d8\u5316\u7387\u7684\u542b\u4e49\u5c31\u76f8\u5f53\u4e8e<span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u884d\u751f\u54c1\/\">\u51fd\u6570\u5bfc\u6570\u7684\u6982\u5ff5<\/a><\/span>\u3002\u56e0\u6b64\uff0c\u77ac\u65f6\u53d8\u5316\u7387\u4e5f\u7528\u4e8e\u8ba1\u7b97\u51fd\u6570\u5728\u67d0\u4e00\u70b9\u7684\u5bfc\u6570\u503c\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-tasa-de-variacion\"><\/span>\u5df2\u89e3\u51b3\u53d8\u5316\u7387\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u8ba1\u7b97\u4e0b\u5217\u51fd\u6570\u5728\u533a\u95f4[1,3]\u5185\u7684\u53d8\u5316\u7387\u503c\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-52242e9edb560029e6861be262dc3418_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2-5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"106\" style=\"vertical-align: -5px;\"><\/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\u786e\u5b9a\u51fd\u6570\u5728\u533a\u95f4\u672b\u7aef\u7684\u503c\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-a68e7a97d5a6f45ee1d01481fe687da1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(1)=1^2-5=1-5=-4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"214\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a0d6343387ae4a98c94387008c73c791_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(3)=3^2-5=9-5=4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"200\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5e94\u7528\u53d8\u5316\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-c33fec724dd0a5bf45bfec5a911f5bcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TV}[a,b]=f(b)-f(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6ab143c57ef36bb306946cbe760653ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TV}[1,3]=f(3)-f(1)=4-(-4)=4+4=\\bm{8}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"360\" style=\"vertical-align: -5px;\"><\/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>\u8ba1\u7b97\u4ee5\u4e0b\u51fd\u6570\u5728\u533a\u95f4 [1,4] \u5185\u7684\u5e73\u5747\u53d8\u5316\u7387 (TVM)\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-b43717721aa2afd3fbc6d587213bbdef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=2x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\"><\/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\">\u6211\u4eec\u9996\u5148\u8ba1\u7b97\u51fd\u6570\u5728 x=1 \u548c x=4 \u5904\u7684\u56fe\u50cf\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-0877ab6ef765a3944e138081718775cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(4)=2\\cdot4+1=9\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"151\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e2e61642cf8070ce3ae09b2eb3335c4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(1)=2\\cdot 1+1=3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"151\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5e94\u7528\u5e73\u5747\u53d8\u5316\u7387\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-aca6688a94500231cb464ce5ca91685c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVM} [a,b] = \\cfrac{f(b)-f(a)}{b-a}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"191\" 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-55ff356ed3f6444ca49c49e39dd46072_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVM} [1,4] = \\cfrac{f(4)-f(1)}{4-1} = \\cfrac{9-3}{4-1}=\\cfrac{6}{3} = \\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"323\" style=\"vertical-align: -12px;\"><\/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\u4e0b\u5217\u51fd\u6570\u5728\u533a\u95f4[-1.3]\u5185\u7684\u5e73\u5747\u53d8\u5316\u7387\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-a04612aafb771e8771b2810a18e18475_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=(x+1)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"120\" style=\"vertical-align: -5px;\"><\/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\">\u4e3a\u4e86\u786e\u5b9a\u5e73\u5747\u53d8\u5316\u7387\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u8ba1\u7b97 f(-1) \u548c f(3)\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-3da577fe4ac481741007375057aa116e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(3)=(3+1)^2=(4)^2=16\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"213\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8b7269aaa1c01fb9a5e218a0a627483b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-1)=((-1)+1)^2=(0)^2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"246\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u73b0\u5728\u4f7f\u7528\u5e73\u5747\u53d8\u5316\u7387\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-aca6688a94500231cb464ce5ca91685c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVM} [a,b] = \\cfrac{f(b)-f(a)}{b-a}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"191\" 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-080aef07d76e5d8823128118052fb808_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVM} [-1,3] = \\cfrac{f(3)-f(-1)}{3-(-1)} = \\cfrac{16-0}{3+1}=\\cfrac{16}{4} = \\bm{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"369\" 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>\u8ba1\u7b97\u4e0b\u56fe\u6240\u793a\u51fd\u6570\u5728\u533a\u95f4[2,4]\u5185\u7684\u5e73\u5747\u53d8\u5316\u7387\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\/representation-d-une-fonction-quadratique-ou-parabole.webp\" alt=\"\" class=\"wp-image-137\" width=\"290\" height=\"328\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\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\">\u6211\u4eec\u5e94\u7528\u5e73\u5747\u53d8\u5316\u7387\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-aca6688a94500231cb464ce5ca91685c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVM} [a,b] = \\cfrac{f(b)-f(a)}{b-a}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"191\" 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-436fb10e74beb8c2ede9c9ac586d96c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVM} [2,4]=\\cfrac{f(4)-f(2)}{4-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"192\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6b63\u5982\u6211\u4eec\u5728\u516c\u5f0f\u4e2d\u770b\u5230\u7684\uff0c\u6211\u4eec\u9700\u8981\u627e\u5230 f(4) \u548c f(2) \u7684\u503c\u3002\u901a\u8fc7\u67e5\u770b\u51fd\u6570\u7684\u56fe\u5f62\u8868\u793a\u53ef\u4ee5\u8f7b\u677e\u5b8c\u6210\u6b64\u64cd\u4f5c\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-fad0fc656e95d7bc9517693b55a15540_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(4)=5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9e7d13ebd46205da0aa8ff41e5133ba3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(2)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u77e5\u9053\u4e86\u51fd\u6570\u7684\u503c\uff0c\u6211\u4eec\u5c06\u5b83\u4eec\u4ee3\u5165\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-9a84929c02a38e91b072239affa6d9f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVM}[2,4]=\\cfrac{f(4)-f(2)}{4-2}=\\cfrac{5-1}{4-2}=\\cfrac{4}{2}=\\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"323\" style=\"vertical-align: -12px;\"><\/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\u4e0b\u5217\u51fd\u6570\u5728 x=2 \u70b9\u5904\u7684\u77ac\u65f6\u53d8\u5316\u7387\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-9de7457ac9ec3e1599c6f986c5ba57ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=3x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/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\">\u4e3a\u4e86\u786e\u5b9a\u51fd\u6570\u5728 x=2 \u70b9\u5904\u7684\u77ac\u65f6\u53d8\u5316\u7387\uff0c\u6211\u4eec\u5e94\u7528\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-a66c321e96cb1e871b9c7debfee1f4bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVI}(a)=\\lim\\limits_{h \\to 0} \\cfrac{f(a+h)-f(a)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"235\" style=\"vertical-align: -13px;\"><\/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-73ee822823f921f75014cb9b50e47f51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\text{TVI}(2)=\\lim\\limits_{h \\to 0} \\cfrac{f(2+h)-f(2)}{h}=\\\\[4ex]=\\lim\\limits_{h \\to 0} \\cfrac{3(2+h)-3\\cdot 2}{h} =\\\\[4ex]=\\lim\\limits_{h \\to 0} \\cfrac{6+3h-6}{h}= \\lim\\limits_{h \\to 0} \\cfrac{3h}{h} =\\\\[4ex]=\\lim\\limits_{h \\to 0} \\cfrac{3\\cancel{h}}{\\cancel{h}}=\\lim\\limits_{h \\to 0} 3 = \\bm{3}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"239\" width=\"250\" style=\"vertical-align: 0px;\"><\/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>\u786e\u5b9a\u4ee5\u4e0b\u51fd\u6570\u5728 x=1 \u70b9\u5904\u7684\u77ac\u65f6\u53d8\u5316\u7387 (TVI)\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-a64e895ef4284c9ac73729d092f47767_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"106\" style=\"vertical-align: -5px;\"><\/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\">\u6211\u4eec\u5e94\u7528\u77ac\u65f6\u53d8\u5316\u7387\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-ef687e3c0bab81c2a8eaa578fcc41b9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVI} (a) = \\lim\\limits_{h \\to 0} \\cfrac{f(a+h)-f(a)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"235\" style=\"vertical-align: -13px;\"><\/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-9aae03d6907f804a3015daa4ecca1e9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVI} (1) = \\lim\\limits_{h \\to 0} \\cfrac{f(1+h)-f(1)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"233\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7136\u540e\uff0c\u6211\u4eec\u8ba1\u7b97<\/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-59ab22db5134b4e8bc6bbed7ab09bd5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(1+h)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"64\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-32045357853caad8774629c95963835d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(1):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"42\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bcec545e7bbd1d55ba069ac58c7862ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(1+h) = (1+h)^2+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"181\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c5f418d9c95675368ebe7525ad0354ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(1)=1^2+1=1+1=2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"199\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u5728\u6781\u9650\u4e2d\u627e\u5230\u7684\u503c\u66ff\u6362\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-89bedae84e1ece0933ddf522e449e005_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVI} (1) = \\lim\\limits_{h \\to 0} \\cfrac{f(1+h)-f(1)}{h}= \\lim\\limits_{h \\to 0} \\cfrac{(1+h)^2+1-2}{h} =\\lim\\limits_{h \\to 0} \\cfrac{(1+h)^2-1}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"563\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u89e3\u51b3\u4e86\u8457\u540d\u7684\u4ea7\u54c1\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-ef36f072cd7bee2d30936dc5a18bdf7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{h \\to 0} \\cfrac{1^2+h^2+2\\cdot 1 \\cdot h-1}{h}=\\lim\\limits_{h \\to 0} \\cfrac{1+h^2+2h-1}{h}=\\lim\\limits_{h \\to 0} \\cfrac{h^2+2h}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"488\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u8ba9\u6211\u4eec\u5c1d\u8bd5\u89e3\u51b3\u8fd9\u4e2a\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-eada4220b55e8f3f27f6e565244fa430_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{h \\to 0} \\cfrac{h^2+2h}{h}=\\cfrac{0^2+2\\cdot 0}{0} = \\cfrac{0}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"221\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4f46\u662f\u6211\u4eec\u53d1\u73b0\u96f6\u9664\u4ee5\u96f6\u7684\u4e0d\u5b9a\u5f62\u5f0f\uff0c\u56e0\u6b64\u6211\u4eec\u5bf9\u5206\u6570\u5206\u5b50\u7684\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u5e76\u5316\u7b80\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-89248fe68bc38749f3ad45e65d902840_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{h \\to 0} \\cfrac{h^2+2h}{h}=\\lim\\limits_{h \\to 0} \\cfrac{h(h+2)}{h} = \\lim\\limits_{h \\to 0} \\cfrac{\\cancel{h}(h+2)}{\\cancel{h}}= \\lim\\limits_{h \\to 0}(h+2)\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"442\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <span style=\"color:#FF9B28;\">\u27a4<\/span>\u5982\u679c\u60a8\u4e0d\u77e5\u9053<u style=\"text-decoration-color:#FF9B28;\">\u5982\u4f55\u6c42\u89e3\u96f6\u4e4b\u95f4\u7684\u96f6\u4e0d\u786e\u5b9a\u6027<\/u>\uff0c\u60a8\u53ef\u4ee5\u5728\u4e0a\u9762\u7684\u94fe\u63a5\u4e2d\u67e5\u770b<u style=\"text-decoration-color:#FF9B28;\">\u6709\u5173\u5982\u4f55\u6c42\u89e3\u96f6\u4e4b\u95f4\u7684\u96f6\u4e0d\u786e\u5b9a\u6027\u6781\u9650\u7684\u5b8c\u6574\u8bf4\u660e\u3002<\/u><\/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-5467af069ca6192116dee3e32de90ea7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{h \\to 0}(h+2) = 0+2 =\\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"178\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7efc\u4e0a\u6240\u8ff0\uff0c\u51fd\u6570\u5728x=1\u70b9\u5904\u7684\u77ac\u65f6\u53d8\u5316\u7387\u7b49\u4e8e2\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-fbcab0fecbbbe2fbefd80027e8748bda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathbf{TVI} \\bm{(1) = 2}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -5px;\"><\/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>\u6c42\u4e0b\u5217\u51fd\u6570\u5728 x=2 \u70b9\u5904\u7684\u77ac\u65f6\u53d8\u5316\u7387\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-1b3e71aa0e6f65532f0324d35e827180_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=4x^2-x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"147\" style=\"vertical-align: -5px;\"><\/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\">\u6211\u4eec\u9996\u5148\u4f7f\u7528\u77ac\u65f6\u53d8\u5316\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-ef687e3c0bab81c2a8eaa578fcc41b9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVI} (a) = \\lim\\limits_{h \\to 0} \\cfrac{f(a+h)-f(a)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"235\" style=\"vertical-align: -13px;\"><\/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-a6a7c9ceda50eea0255d09898ff47cbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVI} (2) = \\lim\\limits_{h \\to 0} \\cfrac{f(2+h)-f(2)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"233\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97<\/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-bd34e7bfca2688fc7047d0cbe546068d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(2+h)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"64\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f026e401162db03299777455b748b308_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(2):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"42\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-79281afbca1e53d72c77a132af8593a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(2+h) = 4(2+h)^2-(2+h)+3=4(2+h)^2-h+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"423\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9260dd17b5ceca44c7ff2d860f0354c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(2) =4\\cdot 2^2-2+3=4\\cdot 4-2+3 =17\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"313\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u5728\u6781\u9650\u4e2d\u627e\u5230\u7684\u503c\u66ff\u6362\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-6ad59f5f751af139656a471bf2a41801_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{TVI} (2) = \\lim\\limits_{h \\to 0} \\cfrac{f(2+h)-f(2)}{h}=\\\\[4ex]=\\lim\\limits_{h \\to 0} \\cfrac{4(2+h)^2-h+1-17}{h}=\\\\[4ex]= \\lim\\limits_{h \\to 0} \\cfrac{4(2+h)^2-h-16}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"190\" width=\"286\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u663e\u7740\u7684\u7b49\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-e358be77d34e9ec7c27433743001162c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{h \\to 0} \\cfrac{4(2^2+h^2+2\\cdot 2 \\cdot h)-h-16}{h}=\\lim\\limits_{h \\to 0} \\cfrac{4(4+h^2+4h)-h-16}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"500\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\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-e7c2b63592b070fa6046376f878d45bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{h \\to 0} \\cfrac{16+4h^2+16h-h-16}{h}=\\lim\\limits_{h \\to 0} \\cfrac{4h^2+15h}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"355\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u8ba9\u6211\u4eec\u5c1d\u8bd5\u89e3\u51b3\u8fd9\u4e2a\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-b9dda4d5e5c5eab8c018f1b46a3da45e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{h \\to 0} \\cfrac{4h^2+15h}{h}=\\cfrac{4\\cdot0^2+15\\cdot 0}{0} = \\cfrac{0}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"269\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4f46\u6211\u4eec\u5f97\u5230\u7684\u4e0d\u786e\u5b9a\u6027\u4e3a\u96f6\u9664\u4ee5\u96f6\uff0c\u56e0\u6b64\u6211\u4eec\u5bf9\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u5e76\u7b80\u5316\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-e0d1213a45968f3137f0c39272cd70dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{h \\to 0} \\cfrac{4h^2+15h}{h}=\\lim\\limits_{h \\to 0} \\cfrac{h(4h+15)}{h}=\\lim\\limits_{h \\to 0} \\cfrac{\\cancel{h}(4h+15)}{\\cancel{h}}= \\lim\\limits_{h \\to 0}(4h+15)\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"513\" style=\"vertical-align: -13px;\"><\/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-5eb4579d04c151866059162480d4c816_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{h \\to 0}(4h+15)=4\\cdot 0+15 =\\bm{15}\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"235\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\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-9181cbd259448ba47e80eb081625ee2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathbf{TVI} \\bm{(2) = 15}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u8fd9\u91cc\u6211\u4eec\u89e3\u91ca\u4ec0\u4e48\u662f\u53d8\u5316\u7387\u3001\u5e73\u5747\u53d8\u5316\u7387\u548c\u77ac\u65f6\u53d8\u5316\u7387\u3002\u60a8\u5c06\u80fd\u591f\u770b\u5230\u51e0\u4e2a\u6709\u5173\u5982\u4f55\u8ba1\u7b97\u53d8\u5316\u7387\u7684\u793a\u4f8b\uff0c\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u901a\u8fc7 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e5%9d%87%e5%92%8c%e7%9e%ac%e6%97%b6%e5%8f%98%e5%8c%96%e7%8e%87\/\"> <span class=\"screen-reader-text\">\u5e73\u5747\u548c\u77ac\u65f6\u53d8\u5316\u7387<\/span> \u67e5\u770b\u5168\u6587 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