{"id":11092,"date":"2024-08-24T16:44:35","date_gmt":"2024-08-24T08:44:35","guid":{"rendered":"http:\/\/www.aiersheng.cc\/?p=11092"},"modified":"2024-08-24T16:44:35","modified_gmt":"2024-08-24T08:44:35","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%86-10","status":"publish","type":"post","link":"https:\/\/www.aiersheng.cc\/?p=11092","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\uff0810\uff09"},"content":{"rendered":"

\u9488\u5bf9\u5e42\u6307\u51fd\u6570\u6781\u9650\u8ba1\u7b97\u7684\u77e5\u8bc6\u70b9\uff0c\u7279\u522b\u662f1^\u221e\u578b\u548c\u221e^0\u30010^0\u578b\uff0c\u6211\u4eec\u53ef\u4ee5\u8fdb\u4e00\u6b65\u7ec6\u5316\u89e3\u9898\u7b56\u7565\uff0c\u5e76\u901a\u8fc7\u793a\u4f8b\u6765\u52a0\u6df1\u7406\u89e3\u3002<\/p>\n

1. 1^\u221e\u578b\u6781\u9650\u8ba1\u7b97<\/h3>\n

\u6807\u51c6\u5316\u65b9\u6cd5\uff1a<\/h4>\n

\u5bf9\u4e8e1^\u221e\u578b\u6781\u9650\uff0c\u6700\u63a8\u8350\u7684\u65b9\u6cd5\u662f\u5c06\u5176\u8f6c\u5316\u4e3a\u00a0limx<\/span>\u2192<\/span>a<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>(<\/span>1<\/span>+<\/span><\/span>u<\/span>(<\/span>x<\/span>)<\/span>)u<\/span>(<\/span>x<\/span>)<\/span><\/span>1<\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0\u7684\u5f62\u5f0f\uff0c\u5176\u4e2d\u00a0u<\/span>(<\/span>x<\/span>)<\/span>\u2192<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u00a0\u5f53\u00a0x<\/span>\u2192<\/span><\/span>a<\/span><\/span><\/span><\/span><\/span>\u3002\u8fd9\u79cd\u65b9\u6cd5\u5229\u7528\u4e86\u7b2c\u4e8c\u4e2a\u91cd\u8981\u6781\u9650\u00a0limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>(<\/span>1<\/span>+<\/span><\/span>x<\/span>)x<\/span><\/span>1<\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>e<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u6ce8\u610f<\/strong>\uff1a\u5728\u8f6c\u5316\u8fc7\u7a0b\u4e2d\uff0c\u4e0d\u80fd\u76f4\u63a5\u5c06\u5e95\u6570\u4e2d\u7684\u90e8\u5206\u9879\u6781\u9650\u7b49\u4e8e1\u5148\u6c42\u51fa\u6765\uff0c\u56e0\u4e3a\u8fd9\u53ef\u80fd\u4f1a\u6539\u53d8\u6574\u4e2a\u8868\u8fbe\u5f0f\u7684\u6781\u9650\u884c\u4e3a\u3002<\/p>\n

\u793a\u4f8b<\/strong>\uff1a\u6c42\u00a0limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>(<\/span>1<\/span>+<\/span><\/span>x<\/span>)s<\/span>i<\/span>n<\/span><\/span>x<\/span><\/span>1<\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u89e3\u7b54<\/strong>\uff1a<\/p>\n

    \n
  1. \u6ce8\u610f\u5230\u00a0sin<\/span>x<\/span>\u2192<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u00a0\u5f53\u00a0x<\/span>\u2192<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\uff0c\u4e14\u00a0s<\/span>i<\/span>n<\/span><\/span>x<\/span><\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u2192<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\uff08\u91cd\u8981\u6781\u9650\u4e4b\u4e00\uff09\u3002<\/li>\n
  2. \u5c06\u539f\u5f0f\u6539\u5199\u4e3a\u00a0limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>(<\/span>1<\/span>+<\/span>x<\/span>)<\/span>x<\/span><\/span>1<\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>s<\/span>i<\/span>n<\/span><\/span>x<\/span><\/span>x<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n
  3. \u5e94\u7528\u7b2c\u4e8c\u4e2a\u91cd\u8981\u6781\u9650\uff0c\u5f97\u00a0limx<\/span>\u2192<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>e<\/span>s<\/span>i<\/span>n<\/span><\/span>x<\/span><\/span>x<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>e<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>e<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ol>\n

    2. \u221e0 \u548c 00 \u578b\u6781\u9650\u8ba1\u7b97<\/h3>\n

    \u53d6\u5bf9\u6570\u6cd5\uff1a<\/h4>\n

    \u5bf9\u4e8e\u8fd9\u4e24\u79cd\u7c7b\u578b\u7684\u6781\u9650\uff0c\u901a\u5e38\u901a\u8fc7\u53d6\u5bf9\u6570\u5c06\u5176\u8f6c\u5316\u4e3a0\u00d7\u221e\u578b\u6216\u5229\u7528\u5bf9\u6570\u6052\u7b49\u5f0f\u8fdb\u884c\u6c42\u89e3\u3002<\/p>\n

    \u793a\u4f8b1<\/strong>\uff1a\u6c42\u00a0limx<\/span>\u2192<\/span>+\u221e<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span>x<\/span><\/span>1<\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

    \u89e3\u7b54<\/strong>\uff1a<\/p>\n

      \n
    1. \u5bf9\u4e24\u8fb9\u53d6\u5bf9\u6570\uff0c\u5f97\u00a0ln<\/span>(<\/span><\/span>limx<\/span>\u2192<\/span>+\u221e<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span>x<\/span><\/span>1<\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/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>ln<\/span>x<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n
    2. \u6ce8\u610f\u5230\u00a0x<\/span><\/span><\/span>l<\/span>n<\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u2192<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u00a0\u5f53\u00a0x<\/span>\u2192<\/span><\/span>+<\/span>\u221e<\/span><\/span><\/span><\/span><\/span>\uff08\u56e0\u4e3a\u5bf9\u6570\u51fd\u6570\u589e\u957f\u6162\u4e8e\u4efb\u4f55\u6b63\u5e42\u51fd\u6570\uff09\u3002<\/li>\n
    3. \u6240\u4ee5\u00a0ln<\/span>(<\/span><\/span>limx<\/span>\u2192<\/span>+\u221e<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span>x<\/span><\/span>1<\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\uff0c\u4ece\u800c\u00a0limx<\/span>\u2192<\/span>+\u221e<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span>x<\/span><\/span>1<\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>e<\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ol>\n

      \u793a\u4f8b2<\/strong>\uff1a\u6c42\u00a0limx<\/span>\u2192<\/span>0+<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

      \u89e3\u7b54<\/strong>\uff08\u4f7f\u7528\u5bf9\u6570\u6052\u7b49\u5f0f\uff09\uff1a<\/p>\n

        \n
      1. \u6ce8\u610f\u5230\u00a0x<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>e<\/span>x<\/span>l<\/span>n<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n
      2. \u5f53\u00a0x<\/span>\u2192<\/span><\/span>0+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0\u65f6\uff0cx<\/span>ln<\/span>x<\/span>\u2192<\/span><\/span>0<\/span>\u00d7<\/span><\/span>(<\/span>\u2212<\/span>\u221e<\/span>)<\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\uff08\u56e0\u4e3a\u00a0ln<\/span>x<\/span>\u2192<\/span><\/span>\u2212<\/span>\u221e<\/span><\/span><\/span><\/span><\/span>\uff09\u3002<\/li>\n
      3. \u6240\u4ee5\u00a0limx<\/span>\u2192<\/span>0+<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>x<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>limx<\/span>\u2192<\/span>0+<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>e<\/span>x<\/span>l<\/span>n<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>e<\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ol>\n

        \u603b\u7ed3<\/h3>\n

        \u5728\u5904\u7406\u5e42\u6307\u51fd\u6570\u6781\u9650\u65f6\uff0c\u5173\u952e\u662f\u8bc6\u522b\u6781\u9650\u7684\u7c7b\u578b\uff08\u59821\u221e\u3001\u221e0\u300100\uff09\u5e76\u9009\u62e9\u5408\u9002\u7684\u89e3\u9898\u65b9\u6cd5\u3002\u5bf9\u4e8e1\u221e\u578b\uff0c\u63a8\u8350\u4f7f\u7528\u6807\u51c6\u5316\u65b9\u6cd5\uff1b\u5bf9\u4e8e\u221e0\u548c00\u578b\uff0c\u5219\u53ef\u4ee5\u901a\u8fc7\u53d6\u5bf9\u6570\u6cd5\u6216\u5229\u7528\u5bf9\u6570\u6052\u7b49\u5f0f\u8fdb\u884c\u6c42\u89e3\u3002\u540c\u65f6\uff0c\u8981\u6ce8\u610f\u907f\u514d\u5728\u6c42\u89e3\u8fc7\u7a0b\u4e2d\u63d0\u524d\u5c06\u90e8\u5206\u9879\u7684\u6781\u9650\u6c42\u51fa\uff0c\u4ee5\u514d\u6539\u53d8\u6574\u4e2a\u8868\u8fbe\u5f0f\u7684\u6781\u9650\u884c\u4e3a\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

        \u9488\u5bf9\u5e42\u6307\u51fd\u6570\u6781\u9650\u8ba1\u7b97\u7684\u77e5\u8bc6\u70b9\uff0c\u7279\u522b\u662f1^\u221e\u578b\u548c\u221e^0\u30010^0\u578b\uff0c\u6211\u4eec\u53ef\u4ee5\u8fdb\u4e00\u6b65\u7ec6\u5316\u89e3\u9898\u7b56\u7565\uff0c\u5e76\u901a\u8fc7\u793a\u4f8b\u6765\u52a0\u6df1\u7406 […]<\/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-11092","post","type-post","status-publish","format-standard","hentry","category-zsb"],"_links":{"self":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/posts\/11092","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=11092"}],"version-history":[{"count":0,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/posts\/11092\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11092"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11092"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11092"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}