{"id":152,"date":"2011-12-01T17:50:32","date_gmt":"2011-12-01T08:50:32","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=152"},"modified":"2021-10-29T10:16:50","modified_gmt":"2021-10-29T01:16:50","slug":"wsr201003","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr201003\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52010\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\\(a , b\\) \u3092\u5b9f\u6570\u3068\u3057, \\(xy\\) \u5e73\u9762\u4e0a\u306e\u6b21\u306e \\(2\\) \u3064\u306e\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306b\u3064\u3044\u3066\u8003\u3048\u308b.\r\n\\[\\begin{align}\r\ny & = e^{|x|} \\quad ... [1] \\\\\r\ny & = ax + b \\quad ... [2]\r\n\\end{align}\\]\r\n\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000[1] , [2] \u304c\u305f\u3060 \\(1\\) \u3064\u306e\u5171\u6709\u70b9\u3092\u3082\u3064\u3068\u304d, \\(b\\) \u3092 \\(a\\) \u3067\u8868\u3057, \u305d\u306e\u30b0\u30e9\u30d5\u3092 \\(ab\\) \u5e73\u9762\u4e0a\u306b\u56f3\u793a\u305b\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000(1)<\/strong> \u306e\u30b0\u30e9\u30d5\u3092 \\(b = f(a)\\) \u3068\u8868\u3059. \u5b9a\u6570 \\(p\\) \u306b\u5bfe\u3057\u3066,\r\n\\[\r\npa + f(a)\r\n\\]\r\n\u3092\u6700\u5927\u306b\u3059\u308b \\(a\\) \u304a\u3088\u3073\u305d\u306e\u6700\u5927\u5024\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[1] \u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308a, \\(y\\) \u8ef8\u306b\u3064\u3044\u3066\u5bfe\u79f0\u3067\u3042\u308b.<\/p>\r\n\"waseda2010_03_01\"\r\n

    \u307e\u305f\r\n\\[\r\n\\displaystyle\\lim _ {x \\rightarrow +0} e^{|x|} = 1 , \\ \\displaystyle\\lim _ {x \\rightarrow -0} e^{|x|} = -1\r\n\\]\r\n\u306b\u6ce8\u610f\u3057\u3066, \u5834\u5408\u5206\u3051\u3057\u3066\u8003\u3048\u308b.<\/p>\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(-1 \\lt a \\lt 1\\) \u306e\u3068\u304d
      \r\n\u6761\u4ef6\u3092\u307f\u305f\u3059\u306e\u306f\r\n\\[\r\nb = e^0 = 1\r\n\\]<\/li>\r\n

    2. 2*<\/strong>\u3000\\(a \\geqq 1\\) \u306e\u3068\u304d
      \r\n\u6761\u4ef6\u3092\u307f\u305f\u3059\u306e\u306f, \u305f\u3060 \\(1\\) \u3064\u306e\u5171\u6709\u70b9\u306e \\(x\\) \u5ea7\u6a19\u306f\u6b63\u306e\u3068\u304d.
      \r\n\u3057\u305f\u304c\u3063\u3066, [1] [2] \u3088\u308a\r\n\\[\r\ne^x - ax = b \\quad ... [\\text{A}]\r\n\\]\r\n\u304c\u305f\u3060 \\(1\\) \u3064\u306e\u89e3\u3092\u3082\u3064\u6761\u4ef6\u3092\u6c42\u3081\u308c\u3070\u3088\u3044.
      \r\n[A] \u306e\u5de6\u8fba\u3092 \\(g(x)\\) \u3068\u304a\u304f\u3068\r\n\\[\r\ng'(x) = e^x -a\r\n\\]\r\n\\(g'(x) = 0\\) \u3092\u89e3\u304f\u3068, \\(x = \\log a\\) .
      \r\n\u3057\u305f\u304c\u3063\u3066\u5897\u6e1b\u8868\u306f\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|cccc} a & 0 & \\cdots & \\log a & \\cdots \\\\ \\hline g'(a) & & - & 0 & + \\\\ \\hline g(a) & 1 & \\searrow & a \\left( 1 -\\log a \\right) & \\nearrow \\\\ \\end{array}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\nb = a \\left( 1 -\\log a \\right)\r\n\\]<\/li>\r\n

    3. 3*<\/strong>\u3000\\(a \\leqq -1\\) \u306e\u3068\u304d
      \r\n[1] \u306e\u5bfe\u79f0\u6027\u3092\u8003\u3048\u308b\u3068, 2*<\/strong>\u306e\u5834\u5408\u304b\u3089\r\n\\[\r\nb = -a \\left\\{ 1 -\\log (-a) \\right\\}\r\n\\]<\/li>\r\n<\/ol>\r\n

      \u4ee5\u4e0a, 1*<\/strong> \uff5e 3*<\/strong> \u3088\u308a\r\n\\[\r\nb = \\underline{ \\left\\{ \\begin{array}{ll} -a \\left\\{ 1 -\\log (-a) \\right\\} & ( \\ a \\leqq -1 \\text{\u306e\u3068\u304d} ) \\\\ 1 & ( \\ -1 \\lt a \\lt 1 \\text{\u306e\u3068\u304d} ) \\\\ a \\left( 1 -\\log a \\right) & ( \\ a \\geqq 1 \\text{\u306e\u3068\u304d} ) \\end{array} \\right. }\r\n\\]\r\n\u307e\u305f, \u3053\u306e\u30b0\u30e9\u30d5\u306f\u4e0b\u56f3<\/p>\r\n\"waseda2010_03_02\"\r\n

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

      \\(h(a) = pa + f(a)\\) \u3068\u304a\u304f.<\/p>\r\n

        \r\n

      1. 1*<\/strong>\u3000\\(p = 0\\) \u306e\u3068\u304d
        \r\n\\(h(a) = f(a)\\) \u306a\u306e\u3067, \\(-1 \\leqq a \\leqq 1\\) \u306e\u3068\u304d, \u6700\u5927\u5024 \\(1\\) \u3092\u3068\u308b.<\/p><\/li>\r\n

      2. 2*<\/strong>\u3000\\(p \\gt 0\\) \u306e\u3068\u304d
        \r\n\\(pa\\) \u306f \\(1\\) \u6b21\u95a2\u6570\u3067\u5358\u8abf\u5897\u52a0\u306a\u306e\u3067, \\(h(a)\\) \u304c\u6700\u5927\u3068\u306a\u308b\u306e\u306f \\(a \\geqq 1\\) \u306e\u7bc4\u56f2\u306b\u3042\u308b.\r\n\\[\r\nh'(a) = p +1 -1 \\cdot \\log a - a \\cdot \\dfrac{1}{a} = p -\\log a\r\n\\]\r\n\\(h(a) = 0\\) \u3092\u89e3\u304f\u3068, \\(a = e^p\\) .\r\n\\[\r\nh(1) = p+1 , \\ h(e^p) = pe^p +e^p (1-p) = e^p\r\n\\]\r\n\u306a\u306e\u3067, \u5897\u6e1b\u8868\u306f\u4e0b\u306e\u901a\u308a.\r\n\\[\r\n\\begin{array}{c|cccc} a & 1 & \\cdots & e^p & \\cdots \\\\ \\hline h'(a) & & + & 0 & - \\\\ \\hline h(a) & p+1 & \\nearrow & e^p & \\searrow \\end{array}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6700\u5927\u5024\u306f\r\n\\[\r\nh(e^p) = e^p\r\n\\]<\/li>\r\n

      3. 3*<\/strong>\u3000\\(p \\lt 0\\) \u306e\u3068\u304d
        \r\n2*<\/strong> \u306e\u5834\u5408\u3068 \\(y\\) \u8ef8\u306b\u3064\u3044\u3066\u5bfe\u79f0\u306a\u306e\u3067, \u6700\u5927\u5024\u306f\r\n\\[\r\nh \\left( -e^{-p} \\right) = e^{-p}\r\n\\]<\/li>\r\n<\/ol>\r\n

        \u4ee5\u4e0a, 1*<\/strong> \uff5e 3*<\/strong> \u3088\u308a<\/p>\r\n