{"id":1300,"date":"2015-10-11T21:45:57","date_gmt":"2015-10-11T12:45:57","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1300"},"modified":"2021-09-29T22:45:15","modified_gmt":"2021-09-29T13:45:15","slug":"tbr201505","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tbr201505\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2015\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\\(f(x) , g(x) , h(x)\\) \u3092\r\n\\[\\begin{align}\r\nf(x) & = \\dfrac{1}{2} ( \\cos x -\\sin x ) \\\\\r\ng(x) & = \\dfrac{1}{\\sqrt{2}} \\sin \\left( x +\\dfrac{\\pi}{4} \\right) \\\\\r\nh(x) & = \\sin x \\\\\r\n\\end{align}\\]\r\n\u3068\u304a\u304f.\r\n\\(3\\) \u3064\u306e\u66f2\u7dda \\(y = f(x)\\) , \\(y = g(x)\\) , \\(y = h(x)\\) \u306e \\(0 \\leqq x \\leqq \\dfrac{\\pi}{2}\\) \u3092\u6e80\u305f\u3059\u90e8\u5206\u3092, \u305d\u308c\u305e\u308c \\(C _ 1 , C _ 2 , C _ 3\\) \u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(C _ 2\\) \u3068 \\(C _ 3\\) \u306e\u4ea4\u70b9\u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(C _ 1\\) \u3068 \\(C _ 3\\) \u306e\u4ea4\u70b9\u306e \\(x\\) \u5ea7\u6a19\u3092 \\(\\alpha\\) \u3068\u3059\u308b. \\(\\sin \\alpha , \\cos \\alpha\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(C _ 1 , C _ 2 , C _ 3\\) \u306b\u3088\u3063\u3066\u56f2\u307e\u308c\u308b\u56f3\u5f62\u306e\u9762\u7a4d\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n

    \\[\r\ng(x) = \\dfrac{1}{2} ( \\sin x +\\cos x )\r\n\\]\r\n\u306a\u306e\u3067, \\(g(x) = h(x)\\) \u3088\u308a\r\n\\[\\begin{align}\r\n\\sin x & = \\cos x \\\\\r\n\\text{\u2234} \\quad x & = \\dfrac{\\pi}{4} \\quad \\left( \\ \\text{\u2235} \\ 0 \\leqq x \\leqq \\dfrac{\\pi}{2} \\ \\right)\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u5ea7\u6a19\u306f\r\n\\[\r\n\\underline{\\left( \\dfrac{\\pi}{4} , \\dfrac{1}{\\sqrt{2}} \\right)}\r\n\\]\r\n

    (2)<\/strong><\/p>\r\n

    \\(f(x) = h(x)\\) \u3088\u308a\r\n\\[\\begin{align}\r\n3 \\sin x -\\cos x & = 0 \\\\\r\n\\sqrt{10} \\sin ( x -\\beta ) & = 0 \\quad ... [1]\r\n\\end{align}\\]\r\n\u305f\u3060\u3057, \\(0 \\lt \\beta \\lt \\dfrac{\\pi}{2}\\) \u3067\r\n\\[\r\n\\sin \\beta = \\dfrac{1}{\\sqrt{10}} , \\ \\cos \\beta = \\dfrac{3}{\\sqrt{10}}\r\n\\]\r\n\\(-\\beta \\leqq x -\\beta \\leqq \\dfrac{\\pi}{2} -\\beta\\) \u306b\u6ce8\u610f\u3057\u3066, [1] \u3092\u3068\u304f\u3068\r\n\\[\r\nx = \\beta\r\n\\]\r\n\u3088\u3063\u3066, \\(\\alpha = \\beta\\) \u306a\u306e\u3067\r\n\\[\r\n\\sin \\alpha = \\underline{\\dfrac{1}{\\sqrt{10}}} , \\ \\cos \\alpha = \\underline{\\dfrac{3}{\\sqrt{10}}}\r\n\\]\r\n

    (3)<\/strong><\/p>\r\n

    \\(f(x) = g(x)\\) \u3092\u3068\u304f\u3068, \\(x = 0\\) .
    \r\n\u3057\u305f\u304c\u3063\u3066, \\(C _ 1 , C _ 2 , C _ 3\\) \u306b\u56f2\u307e\u308c\u305f\u90e8\u5206\u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n\"tbr20150501\"\r\n

    \u3088\u3063\u3066, \u6c42\u3081\u308b\u9762\u7a4d \\(S\\) \u306f\r\n\\[\\begin{align}\r\nS & = \\displaystyle\\int _ 0^{\\frac{\\pi}{4}} g(x) \\, dx -\\displaystyle\\int _ 0^{\\alpha} f(x) \\, dx -\\displaystyle\\int _ {\\alpha}^{\\frac{\\pi}{4}} h(x) \\, dx \\\\\r\n& = \\dfrac{1}{2} \\left[ -\\cos x +\\sin x \\right] _ 0^{\\frac{\\pi}{4}} -\\dfrac{1}{2} \\left[ -\\cos x +\\sin x \\right] _ 0^{\\alpha} -\\left[ -\\cos x \\right] _ 0^{\\frac{\\pi}{4}} \\\\\r\n& = \\dfrac{1}{2} -\\dfrac{1}{2} ( \\sin \\alpha +\\cos \\alpha -1 ) +\\dfrac{1}{\\sqrt{2}} +\\cos \\alpha \\\\\r\n& = \\underline{1 +\\dfrac{1}{\\sqrt{2}} -\\dfrac{5}{\\sqrt{10}}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(f(x) , g(x) , h(x)\\) \u3092 \\[\\begin{align} f(x) & = \\dfrac{1}{2} ( \\cos x -\\sin x ) \\\\ g(x) & = \\dfrac{1}{\\sqrt{ … \u7d9a\u304d\u3092\u8aad\u3080 →<\/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":[132],"tags":[144,137],"class_list":["post-1300","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2015","tag-tsukuba_r","tag-137"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1300","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=1300"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1300\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1300"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1300"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1300"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}