{"id":300,"date":"2012-02-14T00:44:38","date_gmt":"2012-02-13T15:44:38","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=300"},"modified":"2021-09-16T06:46:24","modified_gmt":"2021-09-15T21:46:24","slug":"ngr200803","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ngr200803\/","title":{"rendered":"\u540d\u53e4\u5c4b\u5927\u7406\u7cfb2008\uff1a\u7b2c3\u554f"},"content":{"rendered":"<hr \/>\n<p>\u66f2\u7dda \\(C : \\ y = \\log x\\) \u4e0a\u306e\u70b9 P \\(( a, \\log a )\\) , \u70b9 Q \\(( b, \\log b )\\) \uff08 \\(1 \\lt a \\lt b\\) \uff09\u3092\u3068\u308b.\r\n\u70b9 P , Q \u304b\u3089 \\(x\\) \u8ef8\u306b\u4e0b\u308d\u3057\u305f \\(2\\) \u672c\u306e\u5782\u7dda\u3068 \\(x\\) \u8ef8\u304a\u3088\u3073\u66f2\u7dda \\(C\\) \u3067\u56f2\u307e\u308c\u305f\u90e8\u5206\u306e\u9762\u7a4d\u3092 \\(S\\) \u3068\u3059\u308b. \u70b9 P , Q \u304b\u3089 \\(y\\) \u8ef8\u306b\u4e0b\u308d\u3057\u305f \\(2\\) \u672c\u306e\u5782\u7dda\u3068 \\(y\\) \u8ef8\u304a\u3088\u3073\u66f2\u7dda \\(C\\) \u3067\u56f2\u307e\u308c\u305f\u90e8\u5206\u306e\u9762\u7a4d\u3092 \\(T\\) \u3068\u3059\u308b. \u3053\u306e\u3068\u304d, \\(S = T\\) \u3068\u306a\u308b\u3088\u3046\u306b \\(b\\) \u304c\u3068\u308c\u308b \\(a\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/nagoya_r_2008_03_01.png\" alt=\"\" title=\"nagoya_r_2008_03_01\" class=\"aligncenter size-full\" \/>\r\n<p>\\[\\begin{align}\r\nS & = \\displaystyle\\int _ a^b \\log x \\, dx =\\left[ x \\log x \\right] _ a^b -\\displaystyle\\int _ a^b x \\cdot \\dfrac{1}{x} \\, dx \\\\\r\n& = b \\log b -a \\log a -\\left[ x \\right] _ a^b \\\\\r\n& = b \\log b -a \\log a -(b-a) \\\\\r\nT & = \\displaystyle\\int _ {\\log a}^{\\log b} e^y \\, dy = \\left[ e^y \\right] _ {\\log a}^{\\log b} = b-a\n\\end{align}\\]\r\n\\(S = T\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\nb \\log b -a \\log a -(b-a) & =b-a \\\\\r\n\\text{\u2234} \\quad a \\log a -2a & = b \\log b -2b \\quad ... [1]\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, [1] \u3092\u307f\u305f\u3059 \\(b\\) \u304c\u5b58\u5728\u3059\u308b\u6761\u4ef6\u3092\u8003\u3048\u308c\u3070\u3088\u3044.<br \/>\r\n\u3059\u306a\u308f\u3061, \\(f(x) = x \\log x -2x \\ ( x \\gt 1 )\\) \u3068\u304a\u3044\u305f\u3068\u304d\u306b, \\(f(x) = k\\) \u304c \\(2\\) \u3064\u306e\u7570\u306a\u308b\u89e3 \\(a , b \\ ( a \\lt b )\\) \u3092\u6301\u3064\u3068\u304d\u306e \\(a\\) \u306e\u3068\u308a\u3046\u308b\u5024\u306e\u7bc4\u56f2\u3092\u8003\u3048\u308c\u3070\u3088\u3044.\r\n\\[\r\nf'(x) = \\log x +x \\cdot \\dfrac{1}{x} -2 = \\log x -1\n\\]\r\n\\(f'(x) = 0\\) \u3092\u89e3\u304f\u3068, \\(x = e\\) .<br \/>\r\n\u3057\u305f\u304c\u3063\u3066, \\(f(x)\\) \u306e\u5897\u6e1b\u8868\u306f\u4e0b\u306e\u901a\u308a\u3068\u306a\u308a\r\n\\[\r\n\\begin{array}{c|cccc} x & (1) & \\cdots & e & \\cdots \\\\ \\hline f'(x) & & - & 0 & + \\\\ \\hline f(x) & & \\searrow & \\text{\u6700\u5c0f} & \\nearrow \\end{array}\n\\]\r\n\\(y = f(x)\\) \u306e\u30b0\u30e9\u30d5\u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/nagoya_r_2008_03_02.png\" alt=\"\" title=\"nagoya_r_2008_03_02\" class=\"aligncenter size-full\" \/>\r\n<p>\u3053\u3053\u304b\u3089, \u6c42\u3081\u308b \\(a\\) \u306e\u5024\u306e\u7bc4\u56f2\u306f\r\n\\[\r\n\\underline{1 \\lt a \\lt e}\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u66f2\u7dda \\(C : \\ y = \\log x\\) \u4e0a\u306e\u70b9 P \\(( a, \\log a )\\) , \u70b9 Q \\(( b, \\log b )\\) \uff08 \\(1 \\lt a \\lt b\\) \uff09\u3092\u3068\u308b. \u70b9 P , Q \u304b\u3089 \\ &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/ngr200803\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/span><\/a>","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":[53],"tags":[143,16],"class_list":["post-300","post","type-post","status-publish","format-standard","hentry","category-nagoya_r_2008","tag-nagoya_r","tag-16"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/300","targetHints":{"allow":["GET"]}}],"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=300"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/300\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=300"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=300"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=300"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}