{"id":18209,"date":"2010-12-24T10:45:01","date_gmt":"2010-12-24T02:45:01","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=18209"},"modified":"2021-10-06T16:30:00","modified_gmt":"2021-10-06T08:30:00","slug":"%e7%89%a9%e7%90%86%e8%88%87%e6%95%b8%e5%ad%b8%e3%80%8c%e9%bb%9e%e3%80%8d%e4%b8%8a%e7%9a%84%e5%b7%ae%e7%95%b0%ef%bc%88differences-in-the-point-in-physics-and-mathematics%ef%bc%89","status":"publish","type":"post","link":"http:\/\/localhost\/%e7%89%a9%e7%90%86%e8%88%87%e6%95%b8%e5%ad%b8%e3%80%8c%e9%bb%9e%e3%80%8d%e4%b8%8a%e7%9a%84%e5%b7%ae%e7%95%b0%ef%bc%88differences-in-the-point-in-physics-and-mathematics%ef%bc%89\/","title":{"rendered":"\u7269\u7406\u8207\u6578\u5b78\u300c\u9ede\u300d\u4e0a\u7684\u5dee\u7570"},"content":{"rendered":"

\u7269\u7406\u8207\u6578\u5b78\u300c\u9ede\u300d\u4e0a\u7684\u5dee\u7570 (Differences in the \u201cPoint\u201d in Physics and Mathematics)
\n<\/span>\u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u9644\u5c6c\u9ad8\u7d1a\u4e2d\u5b78\u7269\u7406\u79d1\u9673\u667a\u52dd\u8001\u5e2b\/\u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u7269\u7406\u7cfb\u8521\u5fd7\u7533\u6559\u6388\u8cac\u4efb\u7de8\u8f2f<\/span><\/strong><\/p>\n

\u6578\u5b78\u4e0a\u7684\u9ede (points)\uff0c\u662f\u6307\u7a7a\u9593\u4e0a\u7684\u4e00\u500b\u5ea7\u6a19\u9ede\uff0c\u53ea\u6709\u6a19\u5b9a\u4f4d\u7f6e\uff0c\u8a72\u9ede\u4e0d\u5177\u9ad4\u7a4d\u3002<\/p>\n

\u6578\u5b78\u548c\u7269\u7406\u4e0a\u6709\u610f\u7fa9\u7684\u9ede<\/strong><\/span><\/p>\n

\u7269\u7406\u5b78\u4e0a\u6a19\u5b9a\u7269\u9ad4\u4f4d\u7f6e\u6240\u4f7f\u7528\u7684\u9ede\uff0c\u548c\u6578\u5b78\u7684\u7528\u6cd5\u76f8\u540c\u3002\u4f8b\u5982\uff1a\u7269\u7406\u4e0a\u8ad6\u8ff0\uff0c\u67d0\u7269\u9ad4\u8cea\u5fc3\u4f4d\u7f6e\u5728 $$x=1$$\uff0c\u5373\u4ee3\u8868\u8a72\u7269\u9ad4\u8cea\u5fc3\u6240\u5728\u4f4d\u7f6e\uff0c\u4f4d\u65bc\u5ea7\u6a19\u9ede\u4e0a $$x=1$$\u00a0\u7684\u5730\u65b9\u3002<\/p>\n

\u6578\u5b78\u548c\u7269\u7406\u4e0a\u7121\u610f\u7fa9\u7684\u9ede<\/strong><\/span><\/p>\n

\u82e5\u67d0\u500b\u51fd\u6578\u5728\u8a72\u9ede\u70ba\u4e0d\u9023\u7e8c\uff0c<\/p>\n

\u4ea6\u5373 $$\\lim\\limits_{x\\to a}f(x)\\ne f(a)$$\uff0c\u8a0e\u8ad6 $$f(a)$$ \u7121\u610f\u7fa9\uff0c\u50c5\u80fd\u8a0e\u8ad6\u8a72\u9ede\u7684\u5de6\u53f3\u6975\u9650\u503c $$\\lim\\limits_{x\\to a^+}f(x)$$\u3001$$\\lim\\limits_{x\\to a^-}f(x)$$<\/p>\n

\u7269\u7406\u4e0a\u67d0\u500b\u7269\u7406\u91cf\u5c0d\u7a7a\u9593\u7684\u51fd\u6578\uff0c\u82e5\u5728\u8a72\u9ede\u4e0d\u9023\u7e8c\uff0c\u5247\u5728\u7269\u7406\u4e0a\u8a0e\u8ad6\u8a72\u9ede\u7684\u7269\u7406\u91cf\u662f\u7121\u610f\u7fa9\u7684\u3002\u4f8b\u5982\uff1a\u5747\u52fb\u5e36\u96fb\u91d1\u5c6c\u7403\uff08\u7403\u534a\u5f91\u70ba $$R$$\uff0c\u5e36\u96fb\u91cf $$Q$$\uff09\uff0c<\/p>\n

\u5176\u96fb\u5834\u51fd\u6578\u70ba $$\\left\\{\\begin{array}{ll}E(x)=0&,x<R\\\\E(x)=\\frac{kQ}{x^2}&,x>R\\end{array}\\right.$$<\/p>\n

\u8a0e\u8ad6 $$x=R$$ \u8655\u96fb\u5834\u7121\u610f\u7fa9\uff0c\u50c5\u80fd\u8a0e\u8ad6 $$\\lim\\limits_{x\\to R^+}E(x)=\\frac{kQ}{R^2}$$\uff0c$$\\lim\\limits_{x\\to R^-}E(x)=0$$<\/p>\n

\u7269\u7406\u4e0a\u6709\u610f\u7fa9\u7684\u9ede\uff0c\u4f46\u4e0d\u80fd\u4ee5\u6578\u5b78\u9ede\u89e3\u91cb<\/strong><\/span><\/p>\n

\u7269\u7406\u4e0a\u6240\u63cf\u8ff0\u7684\u300c\u9ede\u300d\u4ecd\u53ef\u4ee5\u5177\u6709\u9ad4\u7a4d\u3001\u8cea\u91cf\u3001\u8868\u9762\u7a4d\u7b49\u7269\u7406\u91cf\u3002\u6b64\u8655\u7684\u9ede\u5728\u505a\u5206\u6790\u4e0a\uff0c\u4e26\u4e0d\u80fd\u5b8c\u5168\u7b49\u540c\u65bc\u6578\u5b78\u4e0a\u4e0d\u8a08\u9ad4\u7a4d\u7684\u5ea7\u6a19\u9ede\u3002<\/p>\n

\u4f8b1\uff1a\u6578\u5b78\u4e0a\u7684\u5169\u500b\u9ede\u53ef\u4ee5\u91cd\u758a\uff0c\u4f46\u7269\u7406\u4e0a\u6240\u8a0e\u8ad6\u7684\u8cea\u9ede\uff0c\u5176\u8ddd\u96e2\u4e0d\u53ef\u70ba $$0$$\uff0c\u5018\u82e5\u5982\u6b64\uff0c\u5169\u9ede\u9593\u7684\u842c\u6709\u5f15\u529b $$\\frac{GMm}{R^2}=\\infty$$\uff0c\u4e26\u4e0d\u5408\u7406\u3002<\/p>\n

\u4f8b2\uff1a\u7269\u7406\u4e0a\u63a2\u8a0e\u6db2\u9762\u4e0b\u67d0\u500b\u9ede\u7684\u58d3\u529b\uff0c\u4ecd\u5047\u8a2d\u8a72\u9ede\u5177\u6709\u9ad4\u7a4d\uff0c\u56e0\u6b64\u4e0a\u4e0b\u5de6\u53f3\u5404\u9762\u7686\u53ef\u8a08\u7b97\u5176\u58d3\u529b\u3002\u4ee5\u6578\u5b78\u65b9\u7a0b\u5f0f\u8868\u9054\u8a72\u9ede\u7684\u58d3\u529b\u5373 $$P=\\displaystyle\\lim_{\\vartriangle{A}\\rightarrow{0}}\\frac{F_{\\perp}}{A}$$\u3002\u82e5\u4ee5\u6578\u5b78\u7684\u9ede\u4f86\u770b\uff0c\u8a72\u9ede\u7684\u9762\u7a4d\u70ba $$0$$\uff0c\u5247 $$P=\\frac{F_{\\perp}}{A}$$ \u7121\u610f\u7fa9\u3002<\/p>\n

\u4f8b3\uff1a\u5e73\u884c\u5149\u7d93\u904e\u8584\u900f\u93e1\u6703\u805a\u65bc\u5c4f\u5e55\u7126\u9ede\u4e0a\uff0c\u4f46\u5c4f\u5e55\u4e0a\u8a72\u9ede\u4ecd\u6709\u9762\u7a4d\u3002\u82e5\u4ee5\u6578\u5b78\u7684\u9ede\u4f86\u770b\uff0c\u5149\u7dda\u6703\u805a\u65bc\u4e00\u9ede\uff0c\u6839\u64da \u7167\u5ea6=\u5149\u901a\u91cf\/\u9762\u7a4d\uff0c\u82e5\u8a72\u9ede\u9762\u7a4d\u70ba $$0$$\uff0c\u5247\u7167\u5ea6\u70ba\u7121\u9650\u5927\u3002<\/p>\n

\u4f8b4\uff1a\u900f\u904e\u7d30\u7e69\u62c9\u4e00\u7269\u9ad4\u4f5c\u7b49\u52a0\u901f\u5ea6\u904b\u52d5\uff0c\u63a2\u8a0e\u7e69\u4e0a\u67d0\u9ede\u5f35\u529b\u3002\u82e5\u4ee5\u6578\u5b78\u9ede\u4f86\u770b\uff0c\u5247\u8a72\u9ede\u5408\u529b\u70ba $$0$$\uff08\u56e0\u70ba $$T_1=T_2$$\uff09\uff0c\u8a72\u9ede\u61c9\u975c\u6b62\u4e0d\u52d5\u3002\u53c8\u8a72\u9ede\u8cea\u91cf\u4ea6\u70ba $$0$$\uff0c\u6839\u64da $$a=\\frac{F}{m}=\\frac{0}{0}$$\uff0c\u7121\u6cd5\u8a08\u7b97\u8a72\u9ede\u52a0\u901f\u5ea6\u5927\u5c0f\u3002<\/p>\n

\u6240\u4ee5\u7528\u6578\u5b78\u7684\u9ede\u4f86\u8a0e\u8ad6\uff0c\u4e0d\u8ad6\u5982\u4f55\u8a0e\u8ad6\uff0c\u7686\u8207\u4e8b\u5be6\u77db\u76fe\u3002\u82e5\u4ee5\u7269\u7406\u89c0\u9ede\u4f86\u770b\u8a72\u9ede\uff0c\u8a72\u9ede\u4ecd\u5177\u8cea\u91cf\uff0c\u8a72\u9ede\u52a0\u901f\u5ea6\u61c9\u70ba\u00a0$$a=\\displaystyle\\lim_{\\vartriangle{m}\\rightarrow{0}}\\frac{T_1-T_2}{m}$$\u3002<\/p>\n

\"\"<\/a><\/p>\n

\u4f8b5\uff1a\u5169\u8cea\u9ede\u9593\u4f5c\u659c\u5411\u5f48\u6027\u78b0\u649e\uff0c\u5df2\u77e5\u8cea\u9ede\u8cea\u91cf\u70ba $$m_1$$\u3001$$m_2$$\uff0c\u521d\u901f\u5ea6\u70ba\u00a0 $$\\bar{v_1}$$\u3001$$\\bar{v_2}$$\u3002<\/p>\n

\u82e5\u5c07\u8cea\u9ede\u8996\u70ba\u6578\u5b78\u4e0a\u7121\u9ad4\u7a4d\u7684\u9ede\uff0c\u5247\u7121\u6cd5\u8a08\u7b97\u51fa\u78b0\u649e\u5f8c\u5169\u8cea\u9ede\u7684\u672b\u901f\uff08\u7121\u552f\u4e00\u89e3\uff09\u3002\u82e5\u8003\u616e\u8cea\u9ede\u534a\u5f91\uff0c\u5c07\u901f\u5ea6\u4f5c\u9023\u5fc3\u7dda\u65b9\u5411\u7684\u5206\u89e3\uff0c\u5373\u53ef\u89e3\u51fa\u5169\u8cea\u9ede\u78b0\u649e\u5f8c\u7684\u672b\u901f\u3002\u5728\u6c23\u9ad4\u52d5\u529b\u8ad6\u4e2d\u7684\u7406\u60f3\u6c23\u9ad4\uff0c\u96d6\u7136\u5047\u5b9a\u6c23\u9ad4\u5206\u5b50\u7684\u9ad4\u7a4d\u53ef\u4ee5\u5ffd\u7565\u4e0d\u8a08\uff0c\u4f46\u5176\u8cea\u9ede\u4ecd\u4e0d\u80fd\u5047\u5b9a\u70ba\u6578\u5b78\u4e0a\u7121\u9ad4\u7a4d\u7684\u9ede\u3002<\/p>\n

\"\"<\/a><\/p>\n

\n

\u53c3\u8003\u8cc7\u6599<\/strong>
\n1.\u7dad\u57fa\u767e\u79d1–\u6975\u9650\uff08\u6578\u5b78\uff09\u00a0\u00a0http:\/\/en.wikipedia.org\/wiki\/Limit_(mathematics)<\/a><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

\u7269\u7406\u8207\u6578\u5b78\u300c\u9ede\u300d\u4e0a\u7684\u5dee\u7570 (Differences in the \u201cPoint\u201d in Physics and…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,107,3],"tags":[612,2193],"class_list":["post-18209","post","type-post","status-publish","format-standard","hentry","category-physics01-02","category-physics00","category-physics01","tag-point","tag-2193","loop-entry","cat-5","cat-107","cat-3","no-thumbnail"],"views":5739,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/18209","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=18209"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/18209\/revisions"}],"predecessor-version":[{"id":89137,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/18209\/revisions\/89137"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=18209"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=18209"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=18209"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}