{"version":"https://jsonfeed.org/version/1.1","title":"苏迟但到的主页","home_page_url":"https://kexohproject.pages.dev","feed_url":"https://kexohproject.pages.dev/json/","description":"<p>你好，欢迎访问个人主页！</p><p>擅长密码学，安全分析，数字水印等技术。</p><p>你可以联系我通过:findmykexin@gmail.com或者知乎私信。</p><p>我的知乎链接：<a href=\"https://www.zhihu.com/people/su-chi-dan-dao\" rel=\"noopener noreferrer\" target=\"_blank\">苏迟但到 - 知乎 (zhihu.com)</a></p><p>我的github链接：<a href=\"https://github.com/kexinoh\" rel=\"noopener noreferrer\" target=\"_blank\">kexinoh</a></p>","icon":"https://kexohcdn.gptapi.cyou/kexohproject/production/images/channel-2e54d141ee195646ca12a9d16507a908.jpg","favicon":"https://kexohcdn.gptapi.cyou/kexohproject/production/images/favicon-340a2925d02a0386f3b954a032834917.jpg","authors":[{"name":"苏迟但到"}],"language":"zh-cn","items":[{"id":"XypcfhMbNHB","title":"如何评价 2021 年各卷高考数学题？有哪些「出其不意」的题和解法？","content_html":"<p data-pid=\"iw-wKq4y\">清理知乎草稿箱23333</p><p data-pid=\"SDIYfbvT\">直接上压轴题了：</p><p data-pid=\"qKvq1KAT\">22.(1)f(x)=x(1-ln x).</p><p data-pid=\"oZB54Mpa\">求单调性。解：省略。</p><p data-pid=\"VlhgLdbY\">（2) <img src=\"https://www.zhihu.com/equation?tex=bIn%5C%2Ca-aIn%5C%2Cb%3Da-b\" alt=\"bIn\\,a-aIn\\,b=a-b\" eeimg=\"1\"/> ,证明 <img src=\"https://www.zhihu.com/equation?tex=2%3C%5Cfrac%7B1%7D%7Ba%7D%2B%5Cfrac%7B1%7D%7Bb%7D%3Ce\" alt=\"2&lt;\\frac{1}{a}+\\frac{1}{b}&lt;e\" eeimg=\"1\"/> .</p><p data-pid=\"Ejz3gl_p\">证： <img src=\"https://www.zhihu.com/equation?tex=bIn%5C%2Ca-aIn+%5C%2Cb%3Da-b%5C%5Cbln%5C%2Ca%2Bb%3DaIn%5C%2Cb%2Ba%5C%5Cb%28Ina%2B1%29%3Da%28Inb%2B1%29%5C%5C+%5Cfrac%7BIna%2B1%7D%7Ba%7D%3D%5Cfrac%7BInb%2B1%7D%7Bb%7D%5C%5C+\" alt=\"bIn\\,a-aIn \\,b=a-b\\\\bln\\,a+b=aIn\\,b+a\\\\b(Ina+1)=a(Inb+1)\\\\ \\frac{Ina+1}{a}=\\frac{Inb+1}{b}\\\\ \" eeimg=\"1\"/> </p><p data-pid=\"qhDZqaMl\">设g(X)=(Inx+1)/x</p><p data-pid=\"fdlZeRq9\">得到当X在（1/e,1)和（1，+oo）上有一个等值点。</p><p data-pid=\"qC1dmA5L\">内心OS分析：我们可以很敏锐的发现a=b=1的时候，就是1/a+1/b=2的时候,a=1/e,b=oo的时候，就是1/a+1/b=e的时候，也就是说我们可以设置一个h(X)=1/a+1/b，其中 <img src=\"https://www.zhihu.com/equation?tex=a%5Cin%281%2Fe%2C1%29\" alt=\"a\\in(1/e,1)\" eeimg=\"1\"/> 之间，h(X)是递减的。</p>","content_text":"清理知乎草稿箱23333\n\n直接上压轴题了：\n\n22.(1)f(x)=x(1-ln x).\n\n求单调性。解：省略。\n\n（2) bIn\\,a-aIn\\,b=a-b\n[https://www.zhihu.com/equation?tex=bIn%5C%2Ca-aIn%5C%2Cb%3Da-b] ,证明\n2<\\frac{1}{a}+\\frac{1}{b}<e\n[https://www.zhihu.com/equation?tex=2%3C%5Cfrac%7B1%7D%7Ba%7D%2B%5Cfrac%7B1%7D%7Bb%7D%3Ce]\n.\n\n证： bIn\\,a-aIn \\,b=a-b\\\\bln\\,a+b=aIn\\,b+a\\\\b(Ina+1)=a(Inb+1)\\\\\n\\frac{Ina+1}{a}=\\frac{Inb+1}{b}\\\\\n[https://www.zhihu.com/equation?tex=bIn%5C%2Ca-aIn+%5C%2Cb%3Da-b%5C%5Cbln%5C%2Ca%2Bb%3DaIn%5C%2Cb%2Ba%5C%5Cb%28Ina%2B1%29%3Da%28Inb%2B1%29%5C%5C+%5Cfrac%7BIna%2B1%7D%7Ba%7D%3D%5Cfrac%7BInb%2B1%7D%7Bb%7D%5C%5C+]\n\n设g(X)=(Inx+1)/x\n\n得到当X在（1/e,1)和（1，+oo）上有一个等值点。\n\n内心OS分析：我们可以很敏锐的发现a=b=1的时候，就是1/a+1/b=2的时候,a=1/e,b=oo的时候，就是1/a+1/b=e的时候，也就是说我们可以设置一个h(X)=1/a+1/b，其中\na\\in(1/e,1) [https://www.zhihu.com/equation?tex=a%5Cin%281%2Fe%2C1%29]\n之间，h(X)是递减的。","date_published":"2022-04-29T08:22:45.000Z","_microfeed":{"web_url":"https://kexohproject.pages.dev/i/2021-XypcfhMbNHB/","json_url":"https://kexohproject.pages.dev/i/XypcfhMbNHB/json/","rss_url":"https://kexohproject.pages.dev/i/XypcfhMbNHB/rss/","guid":"XypcfhMbNHB","status":"published","itunes:title":"New Article Title for iTunes","date_published_short":"Fri Apr 29 2022","date_published_ms":1651220565000}}],"_microfeed":{"microfeed_version":"0.1.2","base_url":"https://kexohproject.pages.dev","categories":[{"name":"Education","categories":[{"name":"Language Learning"}]},{"name":"Technology"}],"subscribe_methods":[{"name":"RSS","type":"rss","url":"https://kexohproject.pages.dev/rss/","image":"https://kexohproject.pages.dev/assets/brands/subscribe/rss.png","enabled":true,"editable":false,"id":"4KlfbtkEfzy"},{"name":"JSON","type":"json","url":"https://kexohproject.pages.dev/json/","image":"https://kexohproject.pages.dev/assets/brands/subscribe/json.png","enabled":true,"editable":false,"id":"DVFm7TYiNSq"}],"description_text":"你好，欢迎访问个人主页！\n\n擅长密码学，安全分析，数字水印等技术。\n\n你可以联系我通过:findmykexin@gmail.com或者知乎私信。\n\n我的知乎链接：苏迟但到 - 知乎 (zhihu.com)\n\n我的github链接：kexinoh","copyright":"©2024","itunes:type":"episodic","items_sort_order":"newest_first"}}