{"id":786,"date":"2013-05-09T22:17:24","date_gmt":"2013-05-09T13:17:24","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=786"},"modified":"2021-03-23T17:16:38","modified_gmt":"2021-03-23T08:16:38","slug":"kyr201304","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr201304\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb2013\uff1a\u7b2c4\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(-\\dfrac{\\pi}{2} \\leqq x \\leqq \\dfrac{\\pi}{2}\\) \u306b\u304a\u3051\u308b \\(\\cos x +\\dfrac{\\sqrt{3}}{4} x^2\\) \u306e\u6700\u5927\u5024\u3092\u6c42\u3081\u3088.\r\n\u305f\u3060\u3057, \\(\\pi \\gt 3.1\\) \u304a\u3088\u3073 \\(\\sqrt{3} \\gt 1.7\\) \u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u306f\u8a3c\u660e\u306a\u3057\u306b\u7528\u3044\u3066\u3088\u3044.<\/p>\r\n<hr>\r\n<!--more-->\r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p>\\(f(x) = \\cos x +\\dfrac{\\sqrt{3}}{4} x^2\\) \u3068\u304a\u304f.\r\n\\[\r\nf(-x) = \\cos x +\\dfrac{\\sqrt{3}}{4} x^2 = f(x)\r\n\\]\r\n\u306a\u306e\u3067, \\(0 \\leqq x \\leqq \\dfrac{\\pi}{2}\\) \u306b\u3064\u3044\u3066\u8abf\u3079\u308c\u3070\u3088\u3044.<br \/>\r\n\\(f(x)\\) \u3092\u5fae\u5206\u3059\u308b\u3068\r\n\\[\r\nf'(x) = -\\sin x +\\dfrac{\\sqrt{3}}{2} x\r\n\\]\r\n\\(f'(x) = 0\\) \u3092\u5909\u5f62\u3059\u308b\u3068\r\n\\[\r\n\\dfrac{\\sqrt{3}}{2} x = \\sin x \\quad ... [1]\r\n\\]\r\n\u3053\u3053\u3067\r\n\\[\\begin{align}\r\n\\dfrac{\\sqrt{3}}{2} \\cdot \\dfrac{\\pi}{2} & \\gt \\dfrac{1.7 \\cdot 3.1}{4} \\\\\r\n& = \\dfrac{5.27}{4} \\gt 1\r\n\\end{align}\\]\r\n\u306a\u306e\u3067, [1] \u306e\u4e21\u8fba\u306e\u30b0\u30e9\u30d5\u3092\u6bd4\u8f03\u3059\u308b\u3068\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308a,<\/p>\r\n<p><img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/kyoto_r_2013_04_01.png\" alt=\"kyoto_r_2013_04_01\" class=\"aligncenter size-full\" \/><\/p>\r\n<p>\\(f'(x) = 0\\) \u306f, \\(0 \\lt x \\lt \\dfrac{\\pi}{2}\\) \u306b\u89e3 \\(x = \\alpha\\) \u30921\u3064\u3060\u3051\u3082\u3064.<br \/>\r\n\u3057\u305f\u304c\u3063\u3066, \\(f(x)\\) \u306e \\(0 \\leqq x \\leqq \\dfrac{\\pi}{2}\\) \u306b\u304a\u3051\u308b\u5897\u6e1b\u306f\u4e0b\u8868\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|ccccc} x & 0 & \\cdots & \\alpha & \\cdots & \\dfrac{\\pi}{2} \\\\ \\hline f'(x) & 0 & - & 0 & + & \\\\ \\hline f(x) & 1 & \\searrow & \\text{\u6700\u5c0f} & \\nearrow & \\dfrac{\\sqrt{3} {\\pi}^2}{16} \\end{array}\r\n\\]\r\n\u3053\u3053\u3067\r\n\\[\\begin{align}\r\n\\dfrac{\\sqrt{3} {\\pi}^2}{16} & \\gt \\dfrac{1.7 \\cdot {3.1}^2}{16} \\\\\r\n& = \\dfrac{16.337}{16} \\gt 1\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u6700\u5927\u5024\u306f \\(x = \\pm \\dfrac{\\pi}{2}\\) \u306e\u3068\u304d\r\n\\[\r\n\\underline{\\dfrac{\\sqrt{3} {\\pi}^2}{16}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(-\\dfrac{\\pi}{2} \\leqq x \\leqq \\dfrac{\\pi}{2}\\) \u306b\u304a\u3051\u308b \\(\\cos x +\\dfrac{\\sqrt{3}}{4} x^2\\) \u306e\u6700\u5927\u5024\u3092\u6c42\u3081\u3088. \u305f\u3060\u3057, \\(\\pi &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kyr201304\/\">\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":[88],"tags":[140,111],"class_list":["post-786","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2013","tag-kyoto_r","tag-111"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/786","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=786"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/786\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=786"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=786"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=786"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}