{"id":1272,"date":"2015-09-11T10:11:48","date_gmt":"2015-09-11T01:11:48","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1272"},"modified":"2021-09-14T20:18:01","modified_gmt":"2021-09-14T11:18:01","slug":"ngr201501","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ngr201501\/","title":{"rendered":"\u540d\u53e4\u5c4b\u5927\u7406\u7cfb2015\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\u6b21\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u95a2\u6570 \\(f(x) = x^{-2} 2^x \\ ( x \\neq 0 )\\) \u306b\u3064\u3044\u3066, \\(f'(x) \\gt 0\\) \u3068\u306a\u308b\u305f\u3081\u306e \\(x\\) \u306b\u95a2\u3059\u308b\u6761\u4ef6\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u65b9\u7a0b\u5f0f \\(2^x = x^2\\) \u306f\u76f8\u7570\u306a\u308b \\(3\\) \u3064\u306e\u5b9f\u6570\u89e3\u3092\u3082\u3064\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u65b9\u7a0b\u5f0f \\(2^x = x^2\\) \u306e\u89e3\u3067\u6709\u7406\u6570\u3067\u3042\u308b\u3082\u306e\u3092\u3059\u3079\u3066\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

    \\(f(x)\\) \u3092\u5fae\u5206\u3059\u308b\u3068\r\n\\[\\begin{align}\r\nf'(x) & = -2 x^{-3} 2^x +x^{-2} \\cdot 2^x \\log 2 \\\\\r\n& = x^{-3} 2^x ( x \\log 2 -2 ) \\ .\r\n\\end{align}\\]\r\n\\(x^{-4} 2^x \\gt 0\\) \u306a\u306e\u3067, \\(f'(x) \\gt 0\\) \u3092\u3068\u304f\u3068\r\n\\[\\begin{gather}\r\nx ( x \\log 2 -2 ) \\gt 0 \\\\\r\n\\text{\u2234} \\quad \\underline{x \\lt 0 , \\ \\dfrac{2}{\\log 2} \\lt x} \\ .\r\n\\end{gather}\\]\r\n

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

    \\(2^x = x^2\\) ... [1] \u3092\u5909\u5f62\u3059\u308b\u3068\r\n\\[\r\nx^{-2} 2^x = f(x) = 1 \\ .\r\n\\]\r\n\u306a\u306e\u3067, \\(y = f(x)\\) \u3068 \\(y = 1\\) \u304c\u7570\u306a\u308b \\(3\\) \u70b9\u3067\u4ea4\u308f\u308b\u3053\u3068\u3092\u793a\u305b\u3070\u3088\u3044.
    \r\n(1)<\/strong> \u306e\u904e\u7a0b\u3068\r\n\\[\r\n\\displaystyle\\lim _ {x \\rightarrow \\infty} f(x) = \\infty , \\ \\displaystyle\\lim _ {x \\rightarrow -\\infty} f(x) = 0 , \\ \\displaystyle\\lim _ {x \\rightarrow \\pm 0} f(x) = \\infty \\ .\r\n\\]\r\n\u3088\u308a, \\(f(x)\\) \u306e\u5897\u6e1b\u306f\u4e0b\u8868\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|ccc} x & ( -\\infty ) & \\cdots & (0) & \\cdots & \\dfrac{2}{\\log 2} & \\cdots & ( \\infty ) \\\\ \\hline f'(x) & & + & & - & 0 & + & \\\\ \\hline f(x) & (0) & \\nearrow & ( \\infty ) & \\searrow & \\text{\u6975\u5c0f} & \\nearrow & ( \\infty ) \\end{array}\r\n\\]\r\n\\(2 \\lt e \\lt 2^2\\) \u3088\u308a, \\(\\dfrac{1}{2} \\lt \\log 2 \\lt 1\\) \u306a\u306e\u3067\r\n\\[\r\n2 \\lt \\dfrac{2}{\\log 2} \\lt 4 \\ .\r\n\\]\r\n\u3067\u3042\u308a\r\n\\[\r\nf(2) = f(4) = 1 \\quad ... [2] \\ .\r\n\\]\r\n\u306a\u306e\u3067 \\(y = f(x)\\) \u306e\u30b0\u30e9\u30d5\u306f, \u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n\"ngr20150101\"\r\n

    \u3088\u3063\u3066, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n

    (3)<\/strong><\/p>\r\n[2] \u3088\u308a, \\(x = 2 , 4\\) \u306f [1] \u306e\u89e3\u3067\u3042\u308b.
    \r\n\\(x \\lt 0\\) \u306a\u308b [1] \u306e\u6709\u7406\u6570\u89e3\u304c\u5b58\u5728\u3059\u308b\u304b\u3092\u8003\u3048\u308b.
    \r\n\u6709\u7406\u6570\u306e\u89e3 \\(x = r \\ ( \\lt 0 )\\) \u304c\u3042\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068, \\(r^2\\) \u306f\u6709\u7406\u6570\u306a\u306e\u3067, \\(2^r\\) \u3082\u6709\u7406\u6570\u3067\u3042\u308b.
    \r\n\u3057\u305f\u304c\u3063\u3066, \u300c \\(r\\) \u306f\u6574\u6570\u3067\u3042\u308b. \u300d... [3]\r\n\u3068\u3053\u308d\u304c, \\(x \\lt 0\\) \u306b\u304a\u3044\u3066, \\(f(x)\\) \u306f\u5358\u8abf\u5897\u52a0\u3067\u3042\u308a\r\n\\[\r\nf(-1) = \\dfrac{1}{2} \\lt 1 \\ .\r\n\\]\r\n\u306a\u306e\u3067, \\(f(x) = 1\\) \u3092\u307f\u305f\u3059\u8ca0\u306e\u6574\u6570 \\(r\\) \u306f\u5b58\u5728\u305b\u305a, [3] \u3068\u77db\u76fe\u3059\u308b.
    \r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u6709\u7406\u6570\u89e3\u306f\r\n\\[\r\nx = \\underline{2 , 4} \\ .\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u6b21\u306e\u554f\u306b\u7b54\u3048\u3088. (1)\u3000\u95a2\u6570 \\(f(x) = x^{-2} 2^x \\ ( x \\neq 0 )\\) \u306b\u3064\u3044\u3066, \\(f'(x) \\gt 0\\) \u3068\u306a\u308b\u305f\u3081\u306e \\(x\\) \u306b\u95a2\u3059\u308b\u6761\u4ef6\u3092\u6c42\u3081\u3088. (2)\u3000\u65b9\u7a0b\u5f0f \\( … \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":[129],"tags":[143,137],"class_list":["post-1272","post","type-post","status-publish","format-standard","hentry","category-nagoya_r_2015","tag-nagoya_r","tag-137"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1272","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=1272"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1272\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1272"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1272"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1272"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}