{"id":11080,"date":"2024-08-24T16:33:43","date_gmt":"2024-08-24T08:33:43","guid":{"rendered":"http:\/\/www.aiersheng.cc\/?p=11080"},"modified":"2024-08-24T16:33:43","modified_gmt":"2024-08-24T08:33:43","slug":"%e6%b5%99%e6%b1%9f%e7%9c%81%e4%b8%93%e5%8d%87%e6%9c%ac%e9%ab%98%e6%95%b0%e5%a4%87%e8%80%83%e5%bf%85%e7%9c%8b%ef%bc%9a%e5%8e%86%e5%b9%b4%e7%9c%9f%e9%a2%98%e6%a0%b8%e5%bf%83%e7%9f%a5%e8%af%86%e7%82%b9-6","status":"publish","type":"post","link":"https:\/\/www.aiersheng.cc\/?p=11080","title":{"rendered":"\u6d59\u6c5f\u7701\u4e13\u5347\u672c\u9ad8\u6570\u5907\u8003\u5fc5\u770b\uff1a\u5386\u5e74\u771f\u9898\u6838\u5fc3\u77e5\u8bc6\u70b9\u5168\u9762\u63d0\u70bc\u4e0e\u4f18\u5316\uff086\uff09"},"content":{"rendered":"

\u9488\u5bf9\u201c\u7279\u5b9a\u7c7b\u578b\u6781\u9650\u8ba1\u7b97\uff08\u542be\u7684x\u6b21\u65b9\u3001lnx\u3001x\u548cn\uff09\u201d\u8fd9\u4e00\u77e5\u8bc6\u70b9\uff0c\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u5e38\u89c1\u7684\u9898\u578b\u548c\u89e3\u9898\u6280\u5de7\u6765\u8bbe\u8ba1\u4f8b\u9898\uff0c\u5e2e\u52a9\u5b66\u751f\u66f4\u597d\u5730\u638c\u63e1\u8fd9\u7c7b\u6781\u9650\u7684\u8ba1\u7b97\u65b9\u6cd5\u3002<\/p>\n

1. \u542be\u7684x\u6b21\u65b9\u7684\u6781\u9650<\/h3>\n

\u4f8b\u98981\uff08\u586b\u7a7a\u9898\uff09<\/strong>\uff1a
\n\u6c42\u6781\u9650\u00a0limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>e<\/span>x<\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u89e3\u7b54<\/strong>\uff1a
\n\u5229\u7528\u6d1b\u5fc5\u8fbe\u6cd5\u5219\uff08\u6216\u7b49\u4ef7\u65e0\u7a77\u5c0f\u66ff\u6362\uff09\uff0c\u6709<\/p>\n

limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>e<\/span>x<\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>(<\/span>e<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>1<\/span>)<\/span>\/<\/span><\/span>d<\/span>x<\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span>=<\/span><\/span>limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>e<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u6216\u5229\u7528\u7b49\u4ef7\u65e0\u7a77\u5c0f\u00a0e<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>1<\/span>\u223c<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\uff08\u5f53\u00a0x<\/span>\u2192<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u00a0\u65f6\uff09\uff0c\u76f4\u63a5\u5f97\u51fa\u7b54\u6848\u4e3a 1\u3002<\/p>\n

2. \u542blnx\u7684\u6781\u9650<\/h3>\n

\u4f8b\u98982\uff08\u8ba1\u7b97\u9898\uff09<\/strong>\uff1a
\n\u6c42\u6781\u9650\u00a0limx<\/span>\u2192<\/span>+\u221e<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>x<\/span><\/span><\/span>l<\/span>n<\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u89e3\u7b54<\/strong>\uff1a
\n\u5229\u7528\u6d1b\u5fc5\u8fbe\u6cd5\u5219\uff0c\u6709<\/p>\n

limx<\/span>\u2192<\/span>+\u221e<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>x<\/span><\/span><\/span>l<\/span>n<\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>=<\/span><\/span>limx<\/span>\u2192<\/span>+\u221e<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>(<\/span>ln<\/span>x<\/span>)<\/span>\/<\/span><\/span>d<\/span>x<\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span>=<\/span><\/span>limx<\/span>\u2192<\/span>+\u221e<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/p>\n

3. \u542bx\u7684\u6781\u9650<\/h3>\n

\u4f8b\u98983\uff08\u8ba1\u7b97\u9898\uff09<\/strong>\uff1a
\n\u6c42\u6781\u9650\u00a0limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>s<\/span>i<\/span>n<\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u89e3\u7b54<\/strong>\uff1a
\n\u5229\u7528\u91cd\u8981\u6781\u9650\u00a0limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>s<\/span>i<\/span>n<\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\uff0c\u76f4\u63a5\u5f97\u51fa\u7b54\u6848\u4e3a 1\u3002<\/p>\n

4. \u542bn\u7684\u6781\u9650\uff08\u6570\u5217\u6781\u9650\uff09<\/h3>\n

\u4f8b\u98984\uff08\u8ba1\u7b97\u9898\uff09<\/strong>\uff1a
\n\u6c42\u6781\u9650\u00a0limn<\/span>\u2192<\/span>\u221e<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>1<\/span>+<\/span>n<\/span><\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u89e3\u7b54<\/strong>\uff1a
\n\u5229\u7528\u6781\u9650\u7684\u5b9a\u4e49\u548c\u6027\u8d28\uff0c\u8be5\u6781\u9650\u662f\u81ea\u7136\u5bf9\u6570\u7684\u5e95\u6570e\u7684\u5b9a\u4e49\uff0c\u5373<\/p>\n

limn<\/span>\u2192<\/span>\u221e<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>1<\/span>+<\/span>n<\/span><\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>e<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u7efc\u5408\u5e94\u7528<\/h3>\n

\u4f8b\u98985\uff08\u8ba1\u7b97\u9898\uff09<\/strong>\uff1a
\n\u6c42\u6781\u9650\u00a0limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span>e<\/span>x<\/span><\/span><\/span><\/span>\u2212<\/span>1\u2212<\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u89e3\u7b54<\/strong>\uff1a
\n\u5229\u7528\u6cf0\u52d2\u5c55\u5f00\u6216\u6d1b\u5fc5\u8fbe\u6cd5\u5219\uff0c\u9996\u5148\u8fdb\u884c\u6cf0\u52d2\u5c55\u5f00\uff1a<\/p>\n

e<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>1<\/span>+<\/span><\/span>x<\/span>+<\/span><\/span>2!<\/span><\/span><\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u22ef<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u6240\u4ee5\uff0c<\/p>\n

limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span>e<\/span>x<\/span><\/span><\/span><\/span>\u2212<\/span>1\u2212<\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span>1+<\/span>x<\/span>+<\/span>2!<\/span><\/span>x<\/span>2<\/span><\/span><\/span>\u200b<\/span>+<\/span>\u22ef<\/span>\u2212<\/span>1\u2212<\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span>2<\/span>x<\/span>2<\/span><\/span><\/span>\u200b<\/span>+<\/span>\u22ef<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>2<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u6216\u4f7f\u7528\u6d1b\u5fc5\u8fbe\u6cd5\u5219\uff1a<\/p>\n

limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span>2<\/span><\/span><\/span><\/span><\/span>e<\/span>x<\/span><\/span><\/span><\/span>\u2212<\/span>1\u2212<\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>2x<\/span><\/span><\/span>e<\/span>x<\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>2<\/span><\/span>e<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>2<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8fd9\u4e9b\u4f8b\u9898\u6db5\u76d6\u4e86\u542be\u7684x\u6b21\u65b9\u3001lnx\u3001x\u548cn\u7684\u7279\u5b9a\u7c7b\u578b\u6781\u9650\u8ba1\u7b97\uff0c\u901a\u8fc7\u7ec3\u4e60\u8fd9\u4e9b\u9898\u76ee\uff0c\u5b66\u751f\u53ef\u4ee5\u66f4\u597d\u5730\u638c\u63e1\u8fd9\u7c7b\u6781\u9650\u7684\u8ba1\u7b97\u65b9\u6cd5\u548c\u6280\u5de7\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u9488\u5bf9\u201c\u7279\u5b9a\u7c7b\u578b\u6781\u9650\u8ba1\u7b97\uff08\u542be\u7684x\u6b21\u65b9\u3001lnx\u3001x\u548cn\uff09\u201d\u8fd9\u4e00\u77e5\u8bc6\u70b9\uff0c\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u5e38\u89c1\u7684\u9898\u578b\u548c\u89e3\u9898\u6280\u5de7\u6765\u8bbe\u8ba1\u4f8b\u9898 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[124],"tags":[],"class_list":["post-11080","post","type-post","status-publish","format-standard","hentry","category-zsb"],"_links":{"self":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/posts\/11080","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=11080"}],"version-history":[{"count":0,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/posts\/11080\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11080"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11080"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11080"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}