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\u516d\u3001WPS\u54ea\u91cc\u6709\u8bba\u6587\u8303\u6587\uff1f<\/h2>\n

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\u7531\u4e8e\u4ee5\u524d\u9009\u62e9\u4e86\u6587\u79d1\uff0c\u6240\u4ee5\u5230\u5927\u5b66\u624d\u63a5\u89e6\u5230\u5371\u673a\u5206\u7684\u77e5\u8bc6\uff0c\u4e5f\u5f00\u59cb\u4e86\u5bf9\u5fae\u79ef\u5206\u7684\u63a2\u7d22\uff0c\u73b0\u5728\u53ef\u4ee5\u8bf4\u662f\u7565\u77e5\u4e00\u3001\u4e8c\u4e86\uff0c\u5728\u6b64\u671f\u95f4\u95f4\u95f4\u7684\u4e86\u89e3\u5230\u5fae\u79ef\u5206\u7684\u7f8e\u597d\uff0c\u4ee5\u53ca\u65b0\u5f15\u529b\u7684\u5f3a\u5927\u3002\u4f46\u5b66\u4e60\u5fae\u79ef\u5206\u7684\u8fc7\u7a0b\u662f\u56f0\u96be\u4e0e\u8270\u8f9b\u7684\uff0c\u4e0e\u6b64\u540c\u65f6\uff0c\u6211\u4e5f\u4e86\u89e3\u5230\u2014\u2014\u6570\u5b66\u662f\u4e00\u79cd\u5bfb\u6c42\u4f17\u6240\u5468\u77e5\u7684\u516c\u7406\u6cd5\u601d\u60f3\u7684\u65b9\u6cd5\uff0c\u8fd9\u79cd\u65b9\u6cd5\u5305\u62ec\u660e\u786e\u7684\u8868\u8ff0\u51fa\u5c06\u8981\u8ba8\u8bba\u7684\u6982\u5ff5\u7684\u542b\u4e49\uff0c\u4ee5\u53ca\u51c6\u786e\u7684\u8868\u8ff0\u51fa\u4f5c\u4e3a\u63a8\u7406\u57fa\u7840\u7684\u516c\u8bbe\u3002\u5177\u6709\u6781\u5176\u4e25\u5bc6\u7684\u903b\u8f91\u601d\u7ef4\u80fd\u529b\u7684\u4eba\u4ece\u8fd9\u4e9b\u5b9a\u4e49\u548c\u516c\u8bbe\u51fa\u53d1\uff0c\u63a8\u5bfc\u51fa\u7ed3\u8bba\u3002\u540c\u65f6\u6570\u5b66\u662f\u4e00\u95e8\u9700\u8981\u521b\u9020\u6027\u7684\u79d1\u5b66\uff0c\u800c\u6570\u5b66\u7684\u8fd9\u4e9b\u521b\u9020\u6027\u7684\u52a8\u529b\u5f80\u5f80\u6765\u81ea\u4e8e\u751f\u6d3b\u3002\u53cd\u8fc7\u6765\uff0c\u6570\u5b66\u7684\u8fd9\u4e9b\u521b\u9020\u6027\u5730\u6210\u679c\u5f80\u5f80\u53c8\u4f5c\u7528\u4e8e\u751f\u6d3b\u7684\u5404\u4e2a\u65b9\u9762\u3002\u4f8b\u5982\uff0c\u5546\u4e1a\u548c\u91d1\u878d\u4e8b\u52a1\u3001\u822a\u6d77\u548c\u5386\u6cd5\u7684\u8ba1\u7b97\u3001\u6865\u6881\u3001\u6c34\u575d\u3001\u6559\u5802\u548c\u4f9b\u7535\u7684\u5efa\u9020\u3001\u4f5c\u6218\u6b66\u5668\u548c\u5de5\u4e8b\u7684\u8bbe\u8ba1\uff0c\u4ee5\u53ca\u8bb8\u591a\u4eba\u7c7b\u7684\u9700\u8981\u3002\u4e0e\u6b64\u540c\u65f6\uff0c\u6570\u5b66\u53c8\u80fd\u5bf9\u8fd9\u4e9b\u95ee\u9898\u7ed9\u51fa\u6700\u5b8c\u6ee1\u7684\u89e3\u51b3\u3002\u5728\u6211\u4eec\u9ad8\u901f\u53d1\u5c55\u7684\u793e\u4f1a\u4e2d\uff0c\u6570\u5b66\u88ab\u5f53\u4f5c\u666e\u904d\u5de5\u5177\u7684\u4e8b\u5b9e\u66f4\u662f\u6bcb\u5eb8\u7f6e\u7591\u7684\u3002<\/p>\n

\u5728\u6211\u4eec\u7684\u65e5\u5e38\u751f\u6d3b\u4e2d\uff0c\u5fae\u79ef\u5206\u786e\u786e\u5b9e\u5b9e\u7684\u5b58\u5728\u7740\uff0c\u53ea\u662f\u6211\u4eec\u7f3a\u5c11\u5584\u4e8e\u53d1\u73b0\u7684\u7cbe\u795e\u800c\u5df2\u3002\u6bd4\u5982\u8bf4\uff0c\u6211\u4eec\u5728\u517b\u82b1\uff0c\u800c\u82b1\u74f6\u4e2d\u6c34\u8fc7\u591a\u4e86\uff0c\u6211\u4eec\u8fd9\u65f6\u5c31\u8981\u5012\u51fa\u90e8\u5206\u6c34\uff0c\u8fd9\u662f\u4e0a\u6d3b\u4e2d\u7684\u516c\u5f0f\u5c31\u4ea7\u751f\u4e86\uff0c\u8fd9\u4e2a\u95ee\u9898\u662f\uff1a\u6211\u4eec\u8981\u5c06\u74f6\u5b50\u503e\u659c\u591a\u5c11\u5ea6\u65f6\u624d\u80fd\u964d\u6c34\u5012\u51fa\u4e00\u534a\u6765\uff1f\u8fd9\u662f\u5fae\u79ef\u5206\u5c31\u6d3e\u4e0a\u7528\u573a\u4e86\u3002<\/p>\n

\u5047\u8bbe\u82b1\u74f6\u7684\u7eb5\u622a\u9762\u662f\u629b\u7269\u7ebf<\/p>\n

Y=ax^2(a>0)<\/p>\n

\u9996\u5148\uff0c\u5148\u7b97\u51fa\u74f6\u5b50\u76f4\u7acb\u6c34\u6ee1\u65f6\u7684\u4f53\u79ef\u7528\u4e00\u4e2a\u79ef\u5206\u5c31\u53ef\u4ee5\u4e86\uff0c\u7ed3\u679c\u7b49\u4e8eV=\u03c0h^2\/(2a);<\/p>\n

\u7b2c\u4e8c\u6b65\uff0c\u5047\u8bbe\u503e\u659c\u89d2\u4e3a\u03b1\uff0c\u6b63\u597d\u5012\u6389\u4e86\u4e00\u534a\u7684\u6c34\uff0c\u91cd\u65b0\u5efa\u7acb\u5750\u6807\u7cfb\uff0c\u4ee4\u6b64\u65f6\u74f6\u7684\u5bf9\u79f0\u8f74\u4e3ay\u8f74\uff0c\u5782\u76f4\u4e8e\u74f6\u7684\u5bf9\u79f0\u8f74\u7684\u5c04\u7ebf\u4e3ax\u8f74\uff0c\u7136\u540e\u5c06\u5750\u6807\u7cfb\u8fd8\u539f\u4e3a\u5e38\u89c4\u6b63\u7acb\u7684\u56fe\u5f62\uff0c\u6b64\u65f6\u74f6\u91cc\u6c34\u7684\u6a2a\u622a\u9762\u56fe\u50cf\u4e3a\u629b\u7269\u7ebf\u548c\u6c34\u9762\u6240\u5728\u76f4\u7ebf\u7684\u516c\u5171\u90e8\u5206\uff0c\u6ce8\u610f\u6b64\u65f6\u6c34\u9762\u6240\u5728\u76f4\u7ebf\u4e0ex\u8f74\u7684\u503e\u89d2\u662f\u521a\u597d\u4e3a\u9898\u76ee\u6240\u63d0\u5230\u7684\u503e\u659c\u89d2\u03b1(\u5982\u539f\u56fe\u6240\u793a\uff0c\u503e\u659c\u540e\u7684\u6c34\u5e73\u9762\u6b64\u65f6\u4e0ex\u8f74\u5e73\u884c\uff0c\u56e0\u6b64\u6c34\u9762\u4e0e\u74f6\u7684\u5bf9\u79f0\u8f74\u7684\u5939\u89d2\u4e3a90-\u03b1\uff0c\u4e5f\u5373\u5728\u65b0\u5efa\u5750\u6807\u7cfb\u4e0b\uff0c\u6c34\u9762\u6240\u5728\u76f4\u7ebf\u4e0ey\u8f74\u7684\u5939\u89d2\u4e5f\u4e3a90-\u03b1\uff0c\u56e0\u6b64\u5b83\u4e0ex\u8f74\u7684\u5939\u89d2\u4e3a\u03b1)\u3002<\/p>\n

\u6240\u4ee5\u53ef\u4ee5\u8bbe\u8be5\u76f4\u7ebf\u65b9\u7a0b\u4e3a<\/p>\n

y=tan\u03b1*x+b<\/p>\n

\u5047\u8bbe\u76f4\u7ebf\u4e0e\u629b\u7269\u7ebf\u7684\u4ea4\u70b9\u4e3aA(x0,y0),B(sqrt(h\/a),h))(\u5de6A,\u53f3B)(B\u70b9\u7684\u7eb5\u5750\u6807\u663e\u7136\u7b49\u4e8e\u74f6\u5b50\u7684\u9ad8\u5ea6h)\uff0c\u5148\u5229\u7528B\u70b9\u5750\u6807\u6c42\u51fa\u76f4\u7ebf\u7684\u622a\u8dddb,\u7136\u540e\u8054\u7acb\u76f4\u7ebf\u4e0e\u629b\u7269\u7ebf\u65b9\u7a0b\u53ef\u4ee5\u6c42\u7684A\u70b9\u5750\u6807\uff1b<\/p>\n

\u7b2c\u4e09\u6b65\uff0c\u5c31\u662f\u6c42\u6b64\u65f6\u74f6\u4e2d\u6c34\u7684\u4f53\u79ef\uff0c\u53ef\u4ee5\u5c06\u56fe\u50cf\u5206\u4e3a\u4e24\u90e8\u5206\uff0c<\/p>\n

\u4e00\u90e8\u5206\u662f\u76f4\u7ebfy=y0\u4e0e\u629b\u7269\u7ebf\u6240\u4ea4\u90e8\u5206\uff0c\u7b2c\u4e8c\u90e8\u5206\u662f\u76f4\u7ebfy=y0\u3001\u76f4\u7ebfy=tan\u03b1*x+b\u53ca\u629b\u7269\u7ebfy=ax^2\uff08a>0)\u76f8\u4ea4\u90e8\u5206\u3002\u7b2c\u4e00\u90e8\u5206\u4f53\u79ef\u4e3aV1=\u222b\u03c0*(x^2)dy=\u222b\u03c0*y\/ady\uff08\u79ef\u5206\u4e0a\u4e0b\u9650\u4e3a0\u548cy0\uff09;<\/p>\n

\u7b2c\u4e8c\u90e8\u5206\u4f53\u79ef\u4e3aV2=\u222b\u03c0*((sqrt(y\/a)-(y-b)\/tan\u03b1)\/2)^2dy(\u79ef\u5206\u4e0a\u4e0b\u9650\u4e3ay0\u548ch);\u56e0\u6b64\u6839\u636e\uff1a V1+V2=V\/2=\u03c0*h^2\/(4a)=\u222b\u03c0*y\/ady\uff08\u79ef\u5206\u4e0a\u4e0b\u9650\u4e3a0\u548cy0\uff09+\u222b\u03c0*((sqrt(y\/a)-(y-b)\/tan\u03b1)\/2)^2dy(\u79ef\u5206\u4e0a\u4e0b\u9650\u4e3ay0\u548ch)\u53ef\u4ee5\u89e3\u5f97\u6240\u6c42\u03b1\u503c\u3002<\/p>\n

\u8fd9\u5c31\u662f\u6570\u5b66\u4e8e\u751f\u6d3b\u7d27\u5bc6\u8054\u7cfb\u5728\u4e00\u8d77\u4e86\uff0c\u5982\u679c\u6570\u5b66\u4e0d\u80fd\u548c\u751f\u6d3b\u7d27\u5bc6\u8054\u7cfb\u5728\u4e00\u8d77\uff0c\u90a3\u4e48\u6570\u5b66\u5c06\u53d8\u5f97\u7a7a\u6d1e\u65e0\u529b\u3002<\/p>\n

\u8457\u540d\u6570\u5b66\u5bb6\u7f57\u7d20\u66fe\u8bf4\uff1a\u201c\u6570\u5b66\u5982\u679c\u6b63\u786e\u770b\u5f85\u4ed6\uff0c\u5219\u5177\u6709\u2026\u2026\u81f3\u9ad8\u65e0\u4e0a\u7684\u7f8e\u2014\u2014\u6b63\u50cf\u96d5\u50cf\u7684\u7f8e\uff0c\u662f\u4e00\u79cd\u51b7\u800c\u4e25\u8083\u7684\u7f8e\uff0c\u8fd9\u79cd\u6bcf\u90e8\u77f3\u5934\u548c\u6211\u4eec\u7684\u5929\u6027\u7684\u5fae\u5f31\u7684\u7f8e\uff0c\u8fd9\u4e9b\u7164\u6ca1\u6709\u7ed8\u753b\u6216\u97f3\u4e50\u7684\u90a3\u4e9b\u534e\u4e3d\u7684\u88c5\u9970\uff0c\u5b83\u53ef\u4ee5\u7eaf\u51c0\u5230\u5d07\u9ad8\u7684\u5730\u6b65\uff0c\u80fd\u591f\u8fbe\u5230\u4e25\u683c\u7684\u53ea\u6709\u6700\u4f1f\u5927\u7684\u827a\u672f\u624d\u80fd\u663e\u793a\u7684\u90a3\u79cd\u5b8c\u7f8e\u7684\u5883\u5730\u3002\u4e00\u79cd\u7cbe\u795e\u4e0a\u7684\u559c\u60a6\uff0c\u4e00\u79cd\u7cbe\u795e\u4e0a\u7684\u4ea2\u594b\uff0c\u4e00\u79cd\u9ad8\u4e8e\u4eba\u7684\u610f\u8bc6\u7684\uff0c\u8fd9\u4e9b\u662f\u81f3\u5584\u81f3\u7f8e\u7684\u6807\u51c6\uff0c\u80fd\u591f\u5728\u8bd7\u91cc\u5f97\u5230\uff0c\u4e5f\u80fd\u591f\u5728\u6570\u5b66\u91cc\u5f97\u5230\u201d\u8fd9\u5c31\u8868\u660e\u4f1f\u5927\u7684\u4eba\u7269\u56e0\u4e3a\u6709\u4e00\u53cc\u5584\u4e8e\u53d1\u73b0\u7f8e\u7684\u773c\u775b\u6240\u4ee5\u4ed6\u770b\u5230\u4e86\u6570\u5b66\u9690\u85cf\u7684\u9b45\u529b\u3002\u9664\u4e86\u521b\u9020\u6027\u548c\u53d1\u73b0\uff0c\u60f3\u8c61\u4e5f\u662f\u53ef\u4ee5\u4f7f\u6570\u5b66\u5728\u6211\u4eec\u601d\u60f3\u4e2d\u5f97\u5230\u5347\u534e\u7684\u3002<\/p>\n

\u5b66\u4e86\u5f88\u4e45\u7684\u6570\u5b66\u4e86\uff0c\u660e\u5356\u5f04\u767e\u6570\u5b66\u7684\u6e90\u8fdc\u6d41\u957f\u4e8e\u9ad8\u6df1\u83ab\u6d4b\uff0c\u4ed6\u5f15\u9886\u7740\u524d\u8fdb\u7684\u9053\u8def\u3002Hankel\uff0cHermann \u8bf4\uff1a\u6570\u5b66\u6cbf\u7740\u4ed6\u81ea\u5df1\u7684\u9053\u8def\u800c\u65e0\u62d8\u65e0\u675f\u7684\u524d\u8fdb\u7740\uff0c\u8fd9\u5e76\u4e0d\u662f\u56e0\u4e3a\u4ed6\u6709\u4ec0\u4e48\u4e0d\u53d7\u6cd5\u5f8b\u7ea6\u675f\u4e4b\u7c7b\u7684\u79cd\u79cd\u8bb8\u53ef\u8bc1\uff0c\u800c\u662f\u56e0\u4e3a\u6570\u5b66\u672c\u6765\u5c31\u5177\u6709\u4e00\u79cd\u7531\u5176\u672c\u6027\u6240\u51b3\u5b9a\u7684\u5e76\u4e14\u4e0e\u5176\u5b58\u5728\u76f8\u7b26\u5408\u7684\u81ea\u7531\u65e0\u76ca\u7684\u662f\u6570\u5b66\u5728\u751f\u6d3b\u4e2d\u72ec\u7279\u800c\u4e0d\u53ef\u6216\u7f3a\uff0c\u5931\u53bb\u4e86\u6570\u5b66\u79d1\u6280\u6c34\u5e73\u5c06\u5012\u9000\u3002\u8fd9\u4e0d\u662f\u8038\u4eba\u542c\u95fb\uff0c\u8fd9\u662f\u5bf9\u6570\u5b66\u8fd9\u95e8\u4f7f\u4eba\u7cbe\u5bc6\u5b66\u79d1\u7684\u80af\u5b9a\uff0c\u8fd9\u662f\u4e0d\u53ef\u7f6e\u5426\u7684\u3002<\/p>\n

\u6570\u5b66\u4e0d\u662f\u89c4\u5f8b\u7684\u53d1\u73b0\u8005\uff0c\u56e0\u4e3a\u5b83\u4e0d\u662f\u5f52\u7eb3\u3002\u6570\u5b66\u4e5f\u4e0d\u662f\u7406\u8bba\u7684\u7f14\u9020\u8005\uff0c\u56e0\u4e3a\u5b83\u4e0d\u662f\u5047\u8bf4\u3002\u4f46\u6570\u5b66\u786e\u5b9e\u89c4\u5f8b\u548c\u5047\u8bf4\u7684\u88c1\u5224\u548c\u4e3b\u5bb0\u8005\uff0c\u56e0\u4e3a\u89c4\u5f8b\u548c\u5047\u8bf4\u90fd\u8981\u5411\u6570\u5b66\u8868\u660e\u81ea\u5df1\u7684\u4e3b\u5f20\uff0c\u7136\u540e\u7b49\u5f85\u6570\u5b66\u7684\u88c1\u5224\u3002\u5982\u679c\u6ca1\u6709\u6570\u5b66\u7684\u8ba4\u53ef\uff0c\u5219\u89c4\u5f8b\u4e0d\u80fd\u8d77\u4f5c\u7528\uff0c\u7406\u8bba\u4e5f\u4e0d\u80fd\u89e3\u91ca\u3002\uff08\u6765\u81ea\u6570\u5b66\u7684\u6587\u5316\uff09<\/p>\n

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