{"id":278,"date":"2012-01-28T21:52:45","date_gmt":"2012-01-28T12:52:45","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=278"},"modified":"2021-09-10T21:16:17","modified_gmt":"2021-09-10T12:16:17","slug":"tok200802","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tok200802\/","title":{"rendered":"\u6771\u5de5\u59272008\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\u5b9f\u6570 \\(x\\) \u306b\u5bfe\u3057, \\(x\\) \u4ee5\u4e0a\u306e\u6700\u5c0f\u306e\u6574\u6570\u3092 \\(f(x)\\) \u3068\u3059\u308b. \\(a , b\\) \u3092\u6b63\u306e\u5b9f\u6570\u3068\u3059\u308b\u3068\u304d, \u6975\u9650\r\n\\[\r\n\\displaystyle\\lim _ {x \\rightarrow \\infty} x^c \\left( \\dfrac{1}{f(ax-7)} -\\dfrac{1}{f(bx+3)} \\right)\r\n\\]\r\n\u304c\u53ce\u675f\u3059\u308b\u3088\u3046\u306a\u5b9f\u6570 \\(c\\) \u306e\u6700\u5927\u5024\u3068, \u305d\u306e\u3068\u304d\u306e\u6975\u9650\u5024\u3092\u6c42\u3081\u3088.<\/p>\r\n

\r\n\r\n

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

\\(D = x^c \\left( \\dfrac{1}{f(ax-7)} -\\dfrac{1}{f(bx+3)} \\right)\\) \u3068\u304a\u304f.
\r\n\u4e00\u822c\u306b, \\(x \\leqq f(x) \\lt x+1\\) \u3068\u306a\u308b\u306e\u3067\r\n\\[\\begin{align}\r\n& \\left\\{ \\begin{array}{l} ax-7 \\leqq f(ax-7) \\lt ax-6 \\\\ bx+3 \\leqq f(bx+3) \\lt bx+4 \\end{array} \\right. \\\\\r\n\\text{\u2234} \\quad & \\left\\{ \\begin{array}{l} \\dfrac{1}{ax-6} \\lt \\dfrac{1}{f(ax-7)} \\leqq \\dfrac{1}{ax-7} \\\\ \\dfrac{1}{bx+4} \\lt \\dfrac{1}{f(bx+3)} \\leqq \\dfrac{1}{bx+3} \\end{array} \\right. \\quad ... [1]\r\n\\end{align}\\]\r\n

    \r\n

  1. 1*<\/strong>\u3000\\(a \\neq b\\) \u306e\u3068\u304d
    \r\n[1] \u3088\u308a\r\n\\[\\begin{align}\r\nx^c \\left( \\dfrac{1}{ax-6} -\\dfrac{1}{bx+3} \\right) & \\lt D \\lt x^c \\left( \\dfrac{1}{ax-7} -\\dfrac{1}{bx+4} \\right) \\\\\r\n\\text{\u2234} \\quad \\dfrac{x^c \\{ (b-a)x +9 \\}}{(ax-6)(bx+3)} & \\lt D \\lt \\dfrac{x^c \\{ (b-a)x +11 \\}}{(ax-7)(bx+4)} \\quad ... [2]\r\n\\end{align}\\]\r\n[2] \u306e\u7b2c \\(1\\) \u8fba, \u7b2c \\(3\\) \u8fba\u306f \\(c \\leqq 1\\) \u306e\u3068\u304d\u53ce\u675f\u3059\u308b.
    \r\n\u7279\u306b \\(c = 1\\) \u306e\u3068\u304d, \\(x \\rightarrow \\infty\\) \u306e\u6975\u9650\u3092\u8003\u3048\u308b\u3068\r\n\\[\\begin{align}\r\n( \\text{\u7b2c1\u8fba} ) & = \\dfrac{b-a +\\frac{9}{x}}{\\left( a -\\frac{6}{x} \\right) \\left( b -\\frac{3}{x} \\right)} \\rightarrow \\dfrac{b-a}{ab} , \\\\\r\n( \\text{\u7b2c3\u8fba} ) & = \\dfrac{b-a +\\frac{11}{x}}{\\left( a -\\frac{7}{x} \\right) \\left( b -\\frac{4}{x} \\right)} \\rightarrow \\dfrac{b-a}{ab}\r\n\\end{align}\\]\r\n\u3086\u3048\u306b, \u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3088\u308a\r\n\\[\r\n\\displaystyle\\lim _ {x \\rightarrow \\infty} D = \\dfrac{b-a}{ab}\r\n\\]<\/li>\r\n

  2. 2*<\/strong>\u3000\\(a = b\\) \u306e\u3068\u304d
    \r\n\\(ax+3 =(ax-7) +10\\) \u306a\u306e\u3067\r\n\\[\r\nf(ax+3) = f(ax-7) +10\r\n\\]\r\n\u3053\u308c\u3092\u7528\u3044\u308c\u3070\r\n\\[\r\n\\dfrac{1}{f(ax-7)} -\\dfrac{1}{f(ax+3)} = \\dfrac{10}{f(ax-7) \\left( f(ax-7) +10 \\right)}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\n\\dfrac{10 x^c}{(ax-7)(ax+3)} \\leqq D \\lt \\dfrac{10 x^c}{(ax-6)(ax+4)} \\quad ... [3]\r\n\\]\r\n[3] \u306e\u7b2c \\(1\\) \u8fba, \u7b2c \\(3\\) \u8fba\u306f \\(c \\leqq 2\\) \u306e\u3068\u304d\u53ce\u675f\u3059\u308b.
    \r\n\u7279\u306b \\(c = 2\\) \u306e\u3068\u304d, \\(x \\rightarrow \\infty\\) \u306e\u6975\u9650\u3092\u8003\u3048\u308b\u3068\r\n\\[\\begin{align}\r\n( \\text{\u7b2c1\u8fba} ) & = \\dfrac{10}{\\left( a -\\frac{7}{x} \\right) \\left( a -\\frac{3}{x} \\right)} \\rightarrow \\dfrac{10}{a^2} , \\\\\r\n( \\text{\u7b2c3\u8fba} ) & = \\dfrac{10}{\\left( a -\\frac{6}{x} \\right) \\left( a -\\frac{4}{x} \\right)} \\rightarrow \\dfrac{10}{a^2}\r\n\\end{align}\\]\r\n\u3086\u3048\u306b, \u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3088\u308a\r\n\\[\r\n\\displaystyle\\lim _ {x \\rightarrow \\infty} D = \\dfrac{10}{a^2}\r\n\\]<\/li>\r\n<\/ol>\r\n

    \u4ee5\u4e0a\u3088\u308a\r\n\\[\r\n\\underline{\\left\\{ \\begin{array}{lll} \\text{\u6700\u5927\u5024} \\ c = 1 , \\quad & \\text{\u6975\u9650\u5024} \\ \\dfrac{b-a}{ab} \\quad & \\ ( \\ a \\neq b \\text{\u306e\u3068\u304d} ) \\\\ \\text{\u6700\u5927\u5024} \\ c = 2 , \\quad & \\text{\u6975\u9650\u5024} \\ \\dfrac{10}{a^2} \\quad & \\ ( \\ a = b \\text{\u306e\u3068\u304d} ) \\end{array} \\right.}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u5b9f\u6570 \\(x\\) \u306b\u5bfe\u3057, \\(x\\) \u4ee5\u4e0a\u306e\u6700\u5c0f\u306e\u6574\u6570\u3092 \\(f(x)\\) \u3068\u3059\u308b. \\(a , b\\) \u3092\u6b63\u306e\u5b9f\u6570\u3068\u3059\u308b\u3068\u304d, \u6975\u9650 \\[ \\displaystyle\\lim _ {x \\rightarrow \\in … \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":[50],"tags":[141,16],"class_list":["post-278","post","type-post","status-publish","format-standard","hentry","category-toko_2008","tag-toko","tag-16"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/278","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=278"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/278\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=278"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=278"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=278"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}