{"id":1341,"date":"2015-12-29T00:45:43","date_gmt":"2015-12-28T15:45:43","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1341"},"modified":"2021-10-30T20:01:35","modified_gmt":"2021-10-30T11:01:35","slug":"tkb201502","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkb201502\/","title":{"rendered":"\u6771\u5927\u6587\u7cfb2015\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(2\\) \u70b9 A \\(( -1 , 1 )\\) , B \\(( 1 , -1 )\\) \u3092\u8003\u3048\u308b.\r\n\u307e\u305f, P \u3092\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e\u70b9\u3068\u3057, \u305d\u306e \\(x\\) \u5ea7\u6a19\u306e\u7d76\u5bfe\u5024\u306f \\(1\\) \u4ee5\u4e0b\u3067\u3042\u308b\u3068\u3059\u308b.\r\n\u6b21\u306e\u6761\u4ef6 (i) \u307e\u305f\u306f (ii) \u3092\u307f\u305f\u3059\u70b9 P \u306e\u7bc4\u56f2\u3092\u56f3\u793a\u3057, \u305d\u306e\u9762\u7a4d\u3092\u6c42\u3081\u3088.<\/p>\r\n

    \r\n

  1. (i)\u3000\u9802\u70b9\u306e \\(x\\) \u5ea7\u6a19\u306e\u7d76\u5bfe\u5024\u304c \\(1\\) \u4ee5\u4e0a\u306e \\(2\\) \u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3067, \u70b9 A , P , B \u3092\u3059\u3079\u3066\u901a\u308b\u3082\u306e\u304c\u3042\u308b.<\/p><\/li>\r\n

  2. (ii)\u3000\u70b9 A , P , B \u306f\u540c\u4e00\u76f4\u7dda\u4e0a\u306b\u3042\u308b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

    \u6761\u4ef6 (ii) \u3092\u307f\u305f\u3059\u70b9 P \u306f, \u76f4\u7dda AB \u4e0a\u306e \\(-1 \\leqq x \\leqq 1\\) \u306e\u90e8\u5206\u3067\u3042\u308a\r\n\\[\r\ny = x \\quad ( -1 \\leqq x \\leqq 1 )\r\n\\]\r\n\u7d9a\u3044\u3066, \u6761\u4ef6 (i) \u3092\u307f\u305f\u3059\u70b9 P \u306f, \\(2\\) \u70b9 A, B \u3092\u901a\u308a, \u9802\u70b9\u306e \\(x\\) \u5ea7\u6a19\u306e\u7d76\u5bfe\u5024\u304c \\(1\\) \u4ee5\u4e0b\u306e\u653e\u7269\u7dda \\(C\\) \u306e \\(-1 \\leqq x \\leqq 1\\) ... [1] \u306e\u90e8\u5206\u3067\u3042\u308b.
    \r\n\u653e\u7269\u7dda \\(y = ax^2 +bx +c \\ (a \\neq 0 )\\) \u304c, \\(2\\) \u70b9 A, B \u3092\u901a\u308b\u3068\u304d\r\n\\[\\begin{align}\r\n-1 & = a +b +c \\\\\r\n1 & = a -b +c \\\\\r\n\\text{\u2234} \\quad b & = -1 , \\quad c = -a\r\n\\end{align}\\]\r\n\u306a\u306e\u3067, \\(C\\) \u306e\u5f0f\u306f\r\n\\[\\begin{align}\r\ny & = ax^2 -x -a \\\\\r\n& = a \\left( x -\\dfrac{1}{2a} \\right)^2 -a -\\dfrac{1}{4a}\r\n\\end{align}\\]\r\n\u6761\u4ef6 (i) \u3088\u308a\r\n\\[\\begin{align}\r\n\\left| \\dfrac{1}{2a} \\right| & \\geqq 1 \\\\\r\n| a | & \\leqq \\dfrac{1}{2} \\\\\r\n\\text{\u2234} \\quad -\\dfrac{1}{2} & \\leqq a \\leqq \\dfrac{1}{2}\r\n\\end{align}\\]\r\n\u3053\u306e\u3068\u304d, \\(C\\) \u306e\u5f0f\u3092 \\(a\\) \u306e\u95a2\u6570\u3068\u307f\u308c\u3070\r\n\\[\r\ny = ( x^2 -1 ) a -x\r\n\\]\r\n[1] \u3088\u308a \\(x^2 -1 \\leqq 0\\) \u306a\u306e\u3067, \u6761\u4ef6\u3092\u6e80\u305f\u3059\u9818\u57df\u306f\r\n\\[\r\n\\dfrac{x^2}{2} -x -\\dfrac{1}{2} \\leqq y \\leqq -\\dfrac{x^2}{2} -x +\\dfrac{1}{2} \\quad ( \\ y = -x \\text{ \u3092\u9664\u304f} )\r\n\\]\r\n\u3088\u3063\u3066, \u70b9 P \u306e\u7bc4\u56f2\u306f\u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u5883\u754c\u542b\u3080\uff09\u3067\u3042\u308a<\/p>\r\n\"tkb20150201\"\r\n

    \u3053\u306e\u9762\u7a4d \\(S\\) \u306f\r\n\\[\\begin{align}\r\nS & = \\displaystyle\\int _ {-1}^1 \\left\\{ \\left( -\\dfrac{x^2}{2} +x -\\dfrac{1}{2} \\right) -\\left( \\dfrac{x^2}{2} +x +\\dfrac{1}{2} \\right) \\right\\} \\, dx \\\\\r\n& = \\dfrac{1}{6} \\cdot 2^3 = \\underline{\\dfrac{4}{3}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(2\\) \u70b9 A \\(( -1 , 1 )\\) , B \\(( 1 , -1 )\\) \u3092\u8003\u3048\u308b. \u307e\u305f, P \u3092\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e\u70b9\u3068\u3057, \u305d\u306e \\(x\\) \u5ea7\u6a19\u306e\u7d76\u5bfe\u5024\u306f \\(1\\) \u4ee5\u4e0b\u3067\u3042\u308b\u3068\u3059\u308b. \u6b21\u306e … \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":[135],"tags":[149,137],"class_list":["post-1341","post","type-post","status-publish","format-standard","hentry","category-tokyo_b_2015","tag-tokyo_b","tag-137"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1341","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=1341"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1341\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1341"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1341"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1341"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}