{"id":669,"date":"2013-03-07T00:40:50","date_gmt":"2013-03-06T15:40:50","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=669"},"modified":"2021-09-29T21:37:20","modified_gmt":"2021-09-29T12:37:20","slug":"thr200703","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr200703\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2007\uff1a\u7b2c3\u554f"},"content":{"rendered":"<hr \/>\n<p>\u81ea\u7136\u6570 \\(n\\) \u306b\u5bfe\u3057, \u65b9\u7a0b\u5f0f\r\n\\[\r\n\\dfrac{1}{x^n} -\\log x -\\dfrac{1}{e} = 0\r\n\\]\r\n\u3092\u8003\u3048\u308b. \u305f\u3060\u3057. \u5bfe\u6570\u306f\u81ea\u7136\u5bfe\u6570\u3067\u3042\u308a, \\(e\\) \u306f\u305d\u306e\u5e95\u3068\u3059\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\u4e0a\u306e\u65b9\u7a0b\u5f0f\u306f \\(x \\geqq 1\\) \u306b\u305f\u3060\u4e00\u3064\u306e\u89e3\u3092\u3082\u3064\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000<strong>(1)<\/strong> \u306e\u89e3\u3092 \\(x _ n\\) \u3068\u3059\u308b. \u3053\u306e\u3068\u304d \\(\\displaystyle\\lim _ {n \\rightarrow \\infty} x _ n = 1\\) \u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n\r\n    <div id='extLink669'>\r\n        <p>\r\n            <a href='https:\/\/www.roundown.net\/nyushi\/thr200703\/' name='ext669' onclick=\"showHide(669,'https:\/\/www.roundown.net\/nyushi\/thr200703\/',this,'entry');return false;\">\u89e3\u7b54\u306f\u3053\u3061\u3089 &#187;<\/a>\r\n        <\/p>\r\n    <\/div>\r\n    <div id='extText669' style='display: none'>\r\n        \r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\\(f(x) = \\dfrac{1}{x^n} -\\log x -\\dfrac{1}{e}\\) \u3068\u304a\u304f.<br \/>\r\n\\(x \\geqq 1\\) \u306b\u304a\u3044\u3066\r\n\\[\\begin{align}\r\nf'(x) & = -\\dfrac{n}{x^{n+1}} -\\dfrac{1}{x} \\\\\r\n& = -\\dfrac{n+x^n}{x^{n+1}} \\lt 0\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(x \\geqq 1\\) \u306b\u304a\u3044\u3066 \\(f(x)\\) \u306f\u5358\u8abf\u6e1b\u5c11\u3067\u3042\u308b.<br \/>\r\n\u3055\u3089\u306b\r\n\\[\\begin{align}\r\nf(1) & = 1 -\\dfrac{1}{e} \\gt 0 , \\\\\r\nf \\left( e^{\\frac{1}{n}} \\right) & = -\\dfrac{1}{n} \\lt 0\r\n\\end{align}\\]\r\n\u3067\u3042\u308b\u304b\u3089, \\(f(x)=0\\) \u306f \\(x \\geqq 1\\) \u306b\u305f\u3060\u4e00\u3064\u306e\u89e3\u3092\u3082\u3064.<\/p>\r\n<p><strong>(2)<\/strong><\/p>\r\n<p><strong>(1)<\/strong> \u306e\u7d50\u679c\u3088\u308a\r\n\\[\r\n1 \\lt x _ n \\lt e^{\\frac{1}{n}}\r\n\\]\r\n\u3053\u3053\u3067\r\n\\[\r\n\\displaystyle\\lim _ {n \\rightarrow \\infty} e^{\\frac{1}{n}} = 1\r\n\\]\r\n\u306a\u306e\u3067, \u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3088\u308a\r\n\\[\r\n\\displaystyle\\lim _ {n \\rightarrow \\infty} x _ n = 1\r\n\\]\r\n\r\n        <p>\r\n            <a href='#ext669' onclick=\"showHide(669,0,this,'entry');return true;\">&#171; \u89e3\u7b54\u3092\u96a0\u3059 <\/a>\r\n        <\/p>\r\n    <\/div>","protected":false},"excerpt":{"rendered":"\u81ea\u7136\u6570 \\(n\\) \u306b\u5bfe\u3057, \u65b9\u7a0b\u5f0f \\[ \\dfrac{1}{x^n} -\\log x -\\dfrac{1}{e} = 0 \\] \u3092\u8003\u3048\u308b. \u305f\u3060\u3057. \u5bfe\u6570\u306f\u81ea\u7136\u5bfe\u6570\u3067\u3042\u308a, \\(e\\) \u306f\u305d\u306e\u5e95\u3068\u3059\u308b. (1)\u3000\u4e0a\u306e [&hellip;]","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[95],"tags":[148,109],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/669"}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=669"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/669\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=669"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=669"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}