{"id":19551,"date":"2011-01-08T16:37:18","date_gmt":"2011-01-08T08:37:18","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=19551"},"modified":"2021-10-06T16:29:34","modified_gmt":"2021-10-06T08:29:34","slug":"%e5%be%ae%e7%a9%8d%e5%88%86%e5%88%9d%e9%9a%8e%ef%bc%8d%e6%ad%b7%e5%8f%b2%e7%99%bc%e5%b1%95%e7%9a%84%e7%9c%bc%e5%85%89%ef%bc%8811%ef%bc%89%e5%be%ae%e5%88%86%e8%88%87%e7%a9%8d%e5%88%86%e7%9a%84%e5%ae%9a","status":"publish","type":"post","link":"http:\/\/localhost\/%e5%be%ae%e7%a9%8d%e5%88%86%e5%88%9d%e9%9a%8e%ef%bc%8d%e6%ad%b7%e5%8f%b2%e7%99%bc%e5%b1%95%e7%9a%84%e7%9c%bc%e5%85%89%ef%bc%8811%ef%bc%89%e5%be%ae%e5%88%86%e8%88%87%e7%a9%8d%e5%88%86%e7%9a%84%e5%ae%9a\/","title":{"rendered":"\u5fae\u7a4d\u5206\u521d\u968e\uff0d\u6b77\u53f2\u767c\u5c55\u7684\u773c\u5149\uff0811\uff09\u5fae\u5206\u8207\u7a4d\u5206\u7684\u5b9a\u7fa9\uff08First Course in Calculus\uff0dA Historical Approach 11. Definitions of Derivative and Integral\uff09"},"content":{"rendered":"<div class=\"pf-content\"><p><span style=\"color: #ff8c00;\"><strong><span style=\"color: #ff6600;\">\u5fae\u7a4d\u5206\u521d\u968e\uff0d\u6b77\u53f2\u767c\u5c55\u7684\u773c\u5149\uff0811\uff09\u5fae\u5206\u8207\u7a4d\u5206\u7684\u5b9a\u7fa9\uff08First Course in Calculus\uff0dA Historical Approach 11. Definitions of Derivative and Integral\uff09<\/span><\/strong><\/span><br \/>\n<span style=\"color: #008000;\"><strong>\u570b\u7acb\u81fa\u7063\u5927\u5b78\u6578\u5b78\u7cfb\u8521\u8070\u660e\u526f\u6559\u6388\/\u570b\u7acb\u81fa\u7063\u5927\u5b78\u6578\u5b78\u7cfb\u8521\u8070\u660e\u526f\u6559\u6388\u8cac\u4efb\u7de8\u8f2f<\/strong><\/span><\/p>\n<p>\u9023\u7d50\uff1a<a href=\"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=19517\">\u5fae\u7a4d\u5206\u521d\u968e\u2014\u6b77\u53f2\u767c\u5c55\u7684\u773c\u5149\uff0810\uff09\u6975\u9650\u3001\u7121\u7aae\u5c0f\u91cf\u8207\u9023\u7e8c\u51fd\u6578<\/a><\/p>\n<p><span style=\"color: #000080;\"><strong>\u7532\u3001\u5fae\u5206<\/strong><\/span><\/p>\n<p>\u63a1\u7528\u6975\u9650\u7684\u8ad6\u8ff0\u6cd5\u4f86\u5b9a\u7fa9\u5c0e\u6578\u5c31\u662f\uff1a<\/p>\n<p style=\"text-align: left;\"><span style=\"color: #800080;\"><strong>\u3010\u5b9a\u7fa9\uff12\u3011<\/strong>\uff08\u5c0e\u6578\u5b9a\u7fa9\u7684\u56db\u90e8\u66f2\uff09<\/span><\/p>\n<p style=\"text-align: left;\">\u7d66\u4e00\u500b\u51fd\u6578 $$y=F(x)$$\uff0c\u6211\u5011\u6309\u4e0b\u5217\u56db\u500b\u6b65\u9a5f\u64cd\u4f5c\uff1a<\/p>\n<ul>\n<li>$$(\\mathrm{i})$$ \u5206\u5272\uff1a\u8b93\u7368\u7acb\u8b8a\u6578 $$x$$ \u8b8a\u5316 $$\\Delta{x}$$ (\u53ef\u6b63\u4e5f\u53ef\u8ca0)<\/li>\n<li>$$(\\mathrm{ii})$$ \u6c42\u5dee\uff1a\u5c0d\u61c9\u7684\u61c9\u8b8a\u6578 $$y$$ \u5c31\u8b8a\u5316 $$\\Delta{y}\\equiv\\Delta{F(x)}\\equiv{F(x+\\Delta{x}-F(x)}$$<\/li>\n<li>$$(\\mathrm{iii})$$ \u6c42\u725b\u9813\u5546\uff1a$$\\Delta{y}\/\\Delta{x}$$<\/li>\n<li>$$(\\mathrm{iv})$$ \u53d6\u6975\u9650\uff1a$$\\displaystyle \\lim_{\\Delta x\\to 0}\\frac{\\Delta y}{\\Delta x}=\\lim_{\\Delta x\\to 0}\\frac{\\Delta F(x)}{\\Delta x}=\\lim_{\\Delta x\\to 0}\\frac{F(x+\\Delta x)-F(x)}{\\Delta x}$$<\/li>\n<\/ul>\n<p>\u5982\u679c\u9019\u500b\u6975\u9650\u503c\u5b58\u5728\uff0c\u5c31\u7a31\u51fd\u6578 $$F$$ \u5728 $$x$$ \u9ede\u70ba<strong>\u53ef\u5fae\u5206<\/strong>\uff08differentiable\uff09\u3002\u8a18\u6b64\u6975\u9650\u503c\u70ba\u00a0$$DF(x)$$\u00a0\u6216\u00a0$$\\frac{dF(x)}{dx}$$\u00a0\u6216\u00a0$$F'(x)$$\uff0c\u4e26\u4e14\u7a31\u70ba $$F$$ \u5728 $$x$$ \u9ede\u7684<strong>\u5c0e\u6578<\/strong>\uff08derivative\uff09\u3002\u5982\u679c\u51fd\u6578 $$F$$ \u5728\u5b9a\u7fa9\u57df\u7684\u6bcf\u4e00\u9ede\u90fd\u53ef\u5fae\u5206\uff0c\u90a3\u9ebc\u6211\u5011\u5c31\u7a31 $$F$$ \u70ba\u4e00\u500b<strong>\u53ef\u5fae\u5206\u51fd\u6578<\/strong>\uff08a differentiable function\uff09\u3002\u5c0e\u6578\u7684\u5e7e\u4f55\u610f\u7fa9\u5c31\u662f\u300c<strong>\u5207\u7dda\u7684\u659c\u7387<\/strong>\u300d\u3002<\/p>\n<p><strong>\u3010\u8a3b\u3011<\/strong>\u5229\u7528\u6975\u9650\u4f86\u8a08\u7b97\u5c0e\u6578\uff0c\u5e38\u898b\u7684\u8b8a\u5f62\u6709\uff1a<\/p>\n<p>$$\\displaystyle DF(x)=\\lim_{\\Delta x\\to 0}\\frac{F(x+\\Delta x)-F(x)}{\\Delta x}=\\lim_{h\\to 0}\\frac{F(x+h)-F(x)}{h}=\\lim_{u\\to x}\\frac{F(u)-F(x)}{u-x}$$<\/p>\n<p>\u63a1\u7528\u7121\u7aae\u5c0f\u91cf\u7684\u8ad6\u8ff0\u6cd5\u4f86\u5b9a\u7fa9\u7684\u5c0e\u6578\u5c31\u662f\uff1a<\/p>\n<p><span style=\"color: #800080;\"><strong>\u3010\u5b9a\u7fa9\uff13\u3011<\/strong>\uff08\u5c0e\u6578\u7684\u5b9a\u7fa9\uff09<\/span><\/p>\n<p style=\"text-align: center;\">$$\\displaystyle DF(x)=\\frac{dF(x)}{dx}=\\frac{F(x+dx)-F(x)}{dx}$$<\/p>\n<p>\u4f46\u5728\u505a\u5be6\u969b\u8a08\u7b97\u6642\uff0c\u8981\u6ce8\u610f\uff1a\u5148\u662f $$dx\\neq{0}$$\uff0c\u7136\u5f8c\u53c8 $$dx=0$$ \u7684\u898f\u5247\u3002<\/p>\n<p><strong>\u3010\u4f8b11\u3011<\/strong>\u8a2d $$F(x)=x^2$$\uff0c\u6c42\u00a0$$DF(x)$$\u3002<br \/>\n<strong>\u3010\u89e3\u7b54\u3011<\/strong><\/p>\n<p>$$(\\mathrm{i})$$ \u7121\u7aae\u5c0f\u91cf\u7684\u8ad6\u8ff0\u6cd5\uff1a<\/p>\n<p style=\"text-align: center;\">$$\\displaystyle DF(x)=\\frac{F(x+dx)-F(x)}{dx}=\\frac{(x+dx)^2-x^2}{dx}=2x+dx=2x$$<br \/>\n\u6216 $$dF(x)=F(x+dx)-F(x)=(x+dx)^2-x^2=2xdx+(dx)^2=2xdx$$<br \/>\n$$(18)$$<\/p>\n<p>\u4e0a\u8ff0\u7684\u6f14\u7b97\u898f\u5247\u662f\uff1a\u7576\u4e00\u500b\u6709\u9650\u91cf\u00a0$$DF(x)$$\u00a0\u662f\u7531\u4e00\u500b\u6709\u9650\u91cf $$2x$$ \u52a0\u4e0a\u4e00\u500b\u7121\u7aae\u5c0f\u91cf $$dx$$ \u6642\uff0c\u662f\u52a0\u4e4b\u4e0d\u589e\u7684\uff0c\u6545 $$2x+dx=2x$$\uff0c\u4ea6\u5373 $$dx$$ \u68c4\u4e4b\u53ef\u4e5f\u3002\u5176\u6b21\uff0c\u7576\u4e00\u500b\u7121\u7aae\u5c0f\u91cf $$dF(x)$$ \u662f\u7531\u4e00\u500b\u7121\u7aae\u5c0f\u91cf $$2xdx$$ \u52a0\u4e0a\u4e00\u500b\u66f4\u9ad8\u968e\u7684\u7121\u7aae\u5c0f\u91cf $$(dx)^2$$ \u6642\uff0c\u5f8c\u8005\u68c4\u4e4b\u53ef\u4e5f\u3002<\/p>\n<p>$$(\\mathrm{ii})$$ \u6975\u9650\u7684\u8ad6\u8ff0\u6cd5\uff1a<\/p>\n<p style=\"padding-left: 30px;\">$$\\begin{array}{ll}DF(x) &amp;=\\lim_{\\Delta x\\to 0}\\frac{F(x+\\Delta x)-F(x)}{\\Delta x}\\\\&amp;\\displaystyle =\\lim_{\\Delta x\\to 0}\\frac{(x+\\Delta x)^2-x^2}{\\Delta x}\\\\&amp;\\displaystyle =\\lim_{\\Delta x\\to 0}(2x+\\Delta x)=2x~~~~~~~~~(19)\\end{array}$$<\/p>\n<p>\u8a31\u591a\u4eba\u7121\u6cd5\u63a5\u53d7\u7121\u7aae\u5c0f\u91cf\u7684\u8ad6\u8ff0\u6cd5\uff0c\u800c\u559c\u6b61\u6975\u9650\u7684\u8ad6\u8ff0\u6cd5\u3002\u5176\u5be6\uff0c\u6211\u5011\u770b\u51fa\u9019\u5169\u7a2e\u8ad6\u8ff0\u6cd5\u662f\u6b8a\u9014\u540c\u6b78\uff0c\u800c\u4e14\u6bd4\u8f03 $$(18)$$ \u8207 $$(19)$$ \u5169\u5f0f\u5c31\u77e5\u6bcf\u4e00\u6b65\u90fd\u6709\u4e92\u76f8\u7684\u5c0d\u7167\u3002\u5728\u79aa\u5b97\u88e1\uff0c\u6709\u300c\u5317\u6f38\u5357\u9813\u300d\u4e4b\u5206\uff0c\u4eff\u6b64\u6211\u5011\u5c31\u8aaa\uff1a\u6975\u9650\u7684\u8ad6\u8ff0\u6cd5\u662f\u300c\u6f38\u609f\u6d3e\u300d\uff0c\u900f\u904e\u6975\u9650\u64cd\u4f5c\u4ee5\u6709\u6daf\u9010\u7121\u6daf\uff1b\u7121\u7aae\u5c0f\u91cf\u7684\u8ad6\u8ff0\u6cd5\u662f\u300c\u9813\u609f\u6d3e\u300d\uff0c\u76f4\u63a5\u98db\u8e8d\u5230\u7121\u6daf\u5f7c\u5cb8\uff0c\u8acb\u51fa\u7121\u7aae\u5c0f\u91cf\uff0c\u5e6b\u5fd9\u5b8c\u6210\u5fae\u5206\u3002<\/p>\n<p><strong>\u3010\u4f8b12\u3011<\/strong>\u7d66\u4e00\u500b\u55ae\u4f4d\u6b63\u65b9\u5f62\uff0c\u5728\u56db\u500b\u89d2\u4e0a\u90fd\u622a\u53bb\u76f8\u540c\u7684\u5c0f\u6b63\u65b9\u5f62\uff0c\u5c07\u5269\u9918\u90e8\u4efd\u6298\u6210\u4e00\u500b\u6c92\u6709\u84cb\u5b50\u7684\u9577\u65b9\u9ad4\u5bb9\u5668\u3002\u6b32\u4f7f\u5176\u5bb9\u7a4d\u70ba\u6700\u5927\uff0c\u6c42\u622a\u53bb\u5c0f\u6b63\u65b9\u5f62\u7684\u908a\u9577\u3002<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/wp-content\/uploads\/2011\/01\/EasyCapture188.bmp\"><img decoding=\"async\" class=\"alignnone size-full wp-image-19581\" title=\"EasyCapture1\" src=\"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/wp-content\/uploads\/2011\/01\/EasyCapture188.bmp\" alt=\"\" \/><\/a><\/p>\n<p><strong>\u3010\u89e3\u7b54\u3011<\/strong>\u5047\u8a2d\u622a\u53bb\u5c0f\u6b63\u65b9\u5f62\u7684\u908a\u9577\u70ba $$x$$\uff0c\u5247\u9577\u65b9\u9ad4\u5bb9\u5668\u7684\u5bb9\u7a4d\u70ba<\/p>\n<p style=\"text-align: center;\">$$V(x)=x(1-2x)^2=4x^3-4x^2+x$$<\/p>\n<p>\u5fae\u5206\uff08\u53c3\u898b\u4f8b4\uff09\u5f97\u5230<\/p>\n<p style=\"text-align: center;\">$$V'(x)=12x^2-8x+1$$<\/p>\n<p>\u89e3\u65b9\u7a0b\u5f0f $$V'(x)=12x^2-8x+1=0$$\uff0c\u5373\u89e3 $$(2x-1)(6x-1)=0$$\uff0c\u5f97\u5230<\/p>\n<p style=\"text-align: center;\">$$\\displaystyle x=\\frac{1}{2}$$ \u6216 $$\\displaystyle x=\\frac{1}{6}$$<\/p>\n<p>\u5176\u4e2d $$x=1\/2$$ \u4e0d\u5408\uff0c\u56e0\u70ba\u6574\u500b\u6b63\u65b9\u5f62\u90fd\u88ab\u622a\u5149\u3002\u56e0\u6b64 $$x=\\frac{1}{6}$$ \u5c31\u662f\u6240\u6c42\u7684\u7b54\u6848\u3002<\/p>\n<p><strong>\u3010\u7fd2\u984c\uff17\u3011<\/strong>\u5728\u534a\u5f91\u70ba $$1$$ \u7684\u7403\u9762\u88e1\uff0c\u5167\u63a5\u4e00\u500b\u6b63\u5713\u9310\u4f7f\u5176\u9ad4\u7a4d\u70ba\u6700\u5927\u3002\u8a66\u6c42\u6b64\u6b63\u5713\u9310\u7684\u5e95\u534a\u5f91\u8207\u9ad8\u3002<\/p>\n<p><span style=\"color: #000080;\"><strong>\u4e59\u3001\u5b9a\u7a4d\u5206<\/strong><\/span><\/p>\n<p><span style=\"color: #800080;\"><strong>\u3010\u5b9a\u7fa94\u3011<\/strong>\uff08\u7a4d\u5206\u5b9a\u7fa9\u7684\u56db\u90e8\u66f2\uff09<\/span><\/p>\n<p>\u7d66\u4e00\u500b\u51fd\u6578 $$y=f(x)$$\uff0c\u6211\u5011\u6309\u4e0b\u5217\u56db\u500b\u6b65\u9a5f\u64cd\u4f5c\uff1a<\/p>\n<ul>\n<li>$$(\\mathrm{i})$$ \u5206\u5272\uff1a$$a=x_1&lt;x_2&lt;x_3&lt;\\mbox{&#8230;}&lt;x_{n+1}=b$$\uff0c\u8a18 $$\\Delta{x_k}\\equiv{x_{k+1}}-x_k$$\uff0c$$k=1,2,\\mbox{&#8230;}n$$<\/li>\n<li>$$(\\mathrm{ii})$$ \u53d6\u6a23\uff1a\u5728\u6bcf\u4e00\u5c0f\u6bb5\u4e2d\u4efb\u53d6\u4e00\u9ede $$\\xi\\in[x_k,x_{k+1}]$$\uff0c$$k=1,2,\\mbox{&#8230;},n$$<\/li>\n<li>$$(\\mathrm{iii})$$ \u6c42\u8fd1\u4f3c\u548c\uff1a$$\\displaystyle \\sum_{k=1}^n f(\\xi_k)\\Delta x_k$$\uff0c\u53eb\u505a Riemann\u548c<\/li>\n<li>$$(\\mathrm{iv})$$ \u53d6\u6975\u9650\uff1a$$\\displaystyle \\lim\\sum_{k=1}^n f(\\xi_k)\\Delta x_k$$\uff0c\u6b64\u5730\u7684\u6975\u9650\u662f\u8b93\u6bcf\u4e00\u500b $$\\Delta{x_k}\\to{0}$$\u3002<\/li>\n<\/ul>\n<p>\u5982\u679c\u6975\u9650 $$\\displaystyle\\lim\\sum_{k=1}^n f(\\xi_k)(x_{k+1}-x_k)$$\u00a0\u5b58\u5728\uff0c\u4e14\u8ddf\u5206\u5272\u8207\u6a23\u672c\u9ede\u7684\u53d6\u6cd5\u7121\u95dc\uff0c\u5247\u7a31\u51fd\u6578 $$f$$ \u5728\u9589\u5340\u9593 $$[a,b]$$ \u4e0a\u70ba<strong>\u53ef\u7a4d\u5206<\/strong>\uff08intergrable\uff09\uff0c\u8a18\u6b64\u6975\u9650\u503c\u70ba $${\\int}_a^b{f(x)}dx$$\u3002<\/p>\n<p>\u3010\u8a3b\u89e3\u3011<\/p>\n<ol>\n<li>\u5fae\u5206\u7684\u5b9a\u7fa9\u662f\uff1a\u5206\u5272\uff0c\u6c42\u5dee\uff0c\u6c42\u725b\u9813\u5546\uff0c\u53d6\u6975\u9650\u3002\u7a4d\u5206\u7684\u5b9a\u7fa9\u662f\uff1a\u5206\u5272\uff0c\u53d6\u6a23\uff0c\u6c42\u8fd1\u4f3c\u548c\uff0c\u53d6\u6975\u9650\u3002\u5169\u8005\u540c\u6a23\u90fd\u662f\u56db\u500b\u6b65\u9a5f\u3002\u5176\u5be6\uff0c\u6b64\u5730\u7684\u7a4d\u5206\u56e0\u70ba\u6709\u4e0a\u4e0b\u9650\uff0c\u6240\u4ee5\u61c9\u8a72\u53eb\u505a<strong>\u5b9a\u7a4d\u5206<\/strong>\uff08definite integral\uff09\uff0c\u4ee5\u5225\u65bc\u4ee5\u5f8c\u8981\u4ecb\u7d39\u7684<strong>\u4e0d\u5b9a\u7a4d\u5206<\/strong>\uff08indefinite integral\uff09\u3002<\/li>\n<li>\u5b9a\u7a4d\u5206\u6709\u6642\u9700\u8981\u7528\u4e0d\u540c\u7684\u8b8a\u6578\u4f86\u8868\u9054\uff1a$${\\int}_a^b{f(x)}dx={\\int}_a^b{f(t)dt}={\\int}_a^b{f(u)}du$$\u3002\u56e0\u6b64\u7a4d\u5206\u7684\u8b8a\u6578\u53eb\u505a<strong>\u555e\u8b8a\u6578<\/strong>\uff08Dummy variable\uff09\u3002<\/li>\n<li>\u9762\u7a4d\u7684\u5e7e\u4f55\u89e3\u91cb\uff1a\u82e5 $$f(x)\\geq{0},\\forall{x}\\in[a,b]$$\uff0c\u5247 $${\\int}_a^b{f(x)}dx$$ \u8868\u793a\u7531\u51fd\u6578 $$y=f(x)$$ \u7684\u5716\u5f62\u3001$$x$$ \u8ef8\u3001\u76f4\u7dda $$x=a$$\uff0c$$x=b$$ \u6240\u570d\u6210\u9818\u57df\u7684\u9762\u7a4d\u3002\u4e00\u822c\u60c5\u5f62\uff0c\u7576 $$f(x)$$ \u7684\u503c\u6709\u6b63\u8ca0\u6642\uff0c$${\\int}_a^b|f(x)|dx$$ \u624d\u662f\u9762\u7a4d\u3002<\/li>\n<\/ol>\n<p><span style=\"color: #800080;\"><strong>\u3010\u5b9a\u7406\uff16\u3011<\/strong><\/span>\u82e5\u51fd\u6578 $$y=f(x)$$ \u5728\u9589\u5340\u9593 $$[a,b]$$ \u4e0a\u9023\u7e8c\uff0c\u5247\u5b9a\u7a4d\u5206 $${\\int}_a^b{f(x)}dx$$ \u5b58\u5728\u3002<\/p>\n<p>\u9023\u7d50\uff1a<a href=\"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=19656\" target=\"_blank\"><strong>\u5fae\u7a4d\u5206\u521d\u968e\uff0d\u6b77\u53f2\u767c\u5c55\u7684\u773c\u5149\uff0812\uff09\u5fae\u7a4d\u5206\u5b78\u6839\u672c\u5b9a\u7406<\/strong><\/a><\/p>\n<p>\u53c3\u8003\u6587\u737b\uff1a<\/p>\n<ol>\n<li>\u8521\u8070\u660e\uff1a\u5fae\u7a4d\u5206\u7684\u6b77\u53f2\u6b65\u9053\u3002\u4e09\u6c11\u66f8\u5c40\uff0c\u53f0\u5317\uff0c2009\u3002<\/li>\n<li>\u8521\u8070\u660e\uff1a\u6578\u5b78\u7684\u767c\u73fe\u8da3\u8ac7\uff0c\u7b2c\u4e8c\u7248\uff0c\u7b2c19\u7ae0\u3002\u4e09\u6c11\u66f8\u5c40\uff0c\u53f0\u5317\uff0c2010\u3002<\/li>\n<li>Edward\uff1a\u5fae\u7a4d\u5206\u767c\u5c55\u53f2\uff0c\u51e1\u7570\u51fa\u7248\u793e\uff0c\u6797\u8070\u6e90\u8b6f\u3002<\/li>\n<li>Simons\uff1aCalculus Gems, Brief Lives and Memorable Mathematics.McGraw-Hill, Inc.1992.<\/li>\n<li>Dunham\uff1aThe Calculus Gallery, Masterpieces from Newton to Lebesgue.Princeton University Press,2005.<\/li>\n<li>Toeplitz\uff1aThe Calculus,A Genetic Approach.The University of Chicago Press.1963<\/li>\n<\/ol>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u9019\u88e1\u5206\u5225\u5f9e\u6975\u9650\u8207\u7121\u7aae\u5c0f\u91cf\u4f86\u5b9a\u7fa9\u5c0e\u6578\uff0c\u4e26\u4e14\u7d66\u51fa\u7a4d\u5206\u7684\u5b9a\u7fa9\u3002\u8a31\u591a\u4eba\u7121\u6cd5\u63a5\u53d7\u7121\u7aae\u5c0f\u91cf\u7684\u8ad6\u8ff0\u6cd5\uff0c\u800c\u559c\u6b61\u6975\u9650\u7684\u8ad6\u8ff0\u6cd5\u3002\u5176\u5be6\uff0c\u6211\u5011\u770b\u51fa\u9019\u5169\u7a2e\u8ad6\u8ff0\u6cd5\u662f\u6b8a\u9014\u540c\u6b78\uff0c\u800c\u4e14\u6bd4\u8f03\uff0818\uff09\u8207\uff0819\uff09\u5169\u5f0f\u5c31\u77e5\u6bcf\u4e00\u6b65\u90fd\u6709\u4e92\u76f8\u7684\u5c0d\u7167\u3002\u5728\u79aa\u5b97\u88e1\uff0c\u6709\u300c\u5317\u6f38\u5357\u9813\u300d\u4e4b\u5206\uff0c\u4eff\u6b64\u6211\u5011\u5c31\u8aaa\uff1a\u6975\u9650\u7684\u8ad6\u8ff0\u6cd5\u662f\u300c\u6f38\u609f\u6d3e\u300d\uff0c\u900f\u904e\u6975\u9650\u64cd\u4f5c\u4ee5\u6709\u6daf\u9010\u7121\u6daf\uff1b\u7121\u7aae\u5c0f\u91cf\u7684\u8ad6\u8ff0\u6cd5\u662f\u300c\u9813\u609f\u6d3e\u300d\uff0c\u76f4\u63a5\u98db\u8e8d\u5230\u7121\u6daf\u5f7c\u5cb8\uff0c\u8acb\u51fa\u7121\u7aae\u5c0f\u91cf\uff0c\u5e6b\u5fd9\u5b8c\u6210\u5fae\u5206\u3002<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[233,111],"tags":[785,787,786,784],"class_list":["post-19551","post","type-post","status-publish","format-standard","hentry","category-math08","category-mathematics00","tag-785","tag-787","tag-786","tag-784","loop-entry","cat-233","cat-111","no-thumbnail"],"views":4653,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/19551","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=19551"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/19551\/revisions"}],"predecessor-version":[{"id":88973,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/19551\/revisions\/88973"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=19551"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=19551"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=19551"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}