{"id":393,"date":"2012-05-12T10:33:01","date_gmt":"2012-05-12T01:33:01","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=393"},"modified":"2021-09-09T09:47:38","modified_gmt":"2021-09-09T00:47:38","slug":"osr201205","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/osr201205\/","title":{"rendered":"\u962a\u5927\u7406\u7cfb2012\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\\(1\\) \u500b\u306e\u3055\u3044\u3053\u308d\u3092 \\(3\\) \u56de\u7d9a\u3051\u3066\u6295\u3052\u308b\u3068\u304d, \\(1\\) \u56de\u76ee\u306b\u51fa\u308b\u76ee\u3092 \\(l\\) , \\(2\\) \u56de\u76ee\u306b\u51fa\u308b\u76ee\u3092 \\(m\\) , \\(3\\) \u56de\u76ee\u306b\u51fa\u308b\u76ee\u3092 \\(n\\) \u3067\u8868\u3059\u3053\u3068\u306b\u3059\u308b. \u3053\u306e\u3068\u304d, \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u6975\u9650\u5024\r\n\\[\r\n\\displaystyle\\lim _ {x \\rightarrow -1} \\dfrac{lx^2 +mx +n}{x+1}\n\\]\r\n\u304c\u5b58\u5728\u3059\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u95a2\u6570\r\n\\[\r\nf(x) =\\dfrac{lx^2 +mx +n}{x+1}\n\\]\r\n\u304c, \\(x \\gt -1\\) \u306e\u7bc4\u56f2\u3067\u6975\u5024\u3092\u3068\u308b\u78ba\u7387\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\n\\dfrac{lx^2 +mx +n}{x+1} = lx +m-n +\\dfrac{l-m+n}{x+1}\n\\]\r\n\u306a\u306e\u3067, \u6975\u9650\u5024\u304c\u5b58\u5728\u3059\u308b\u6761\u4ef6\u306f\r\n\\[\\begin{align}\r\nl-m+n & = 0 \\\\\r\n\\text{\u2234} \\quad m & =l+n \\quad ... [1]\n\\end{align}\\]\r\n\\(m \\ ( 2 \\leqq m \\leqq 6 )\\) \u306e\u5024\u306b\u5bfe\u3057\u3066, \\((l,n)\\) \u306e\u7d44\u306f \\(m-1\\) \u7d44\u3042\u308b\u306e\u3067, [1]\u3092\u307f\u305f\u3059 \\(( l, m, n )\\) \u306e\u7d44\u306f\r\n\\[\r\n\\textstyle\\sum\\limits _ {m=2}^{6} (m-1) = \\dfrac{5 \\cdot 6}{2} =15 \\quad \\text{\u7d44}\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n\\dfrac{15}{6^3} = \\underline{\\dfrac{5}{72}}\n\\]\r\n

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

    \\[\\begin{align}\r\nf'(x) & = \\dfrac{(2lx+m)(x+1) -(lx^2+mx+n) \\cdot 1}{(x+1)^2} \\\\\r\n& = \\dfrac{lx^2 +2lx +m-n}{(x+1)^2}\n\\end{align}\\]\r\n\u5206\u5b50\u3092 \\(g(x)\\) \u3068\u304a\u304f\u3068, \\(x \\gt -1\\) \u306b\u304a\u3044\u3066, \\(g(x)\\) \u306e\u7b26\u53f7\u304c\u5909\u5316\u3059\u308b\u6761\u4ef6\u3092\u8003\u3048\u308c\u3070\u3088\u3044.\r\n\\[\r\ng(x) = l (x+1)^2 -l+m-n\n\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\ng(-1) & = -l+m-n \\lt 0 \\\\\r\n\\text{\u2234} \\quad m & \\lt l+n\n\\end{align}\\]\r\n\u80cc\u53cd\u306a\u6761\u4ef6 \\(m \\geqq l+n\\) ...[2] \u3092\u307f\u305f\u3059 \\((l,m,n)\\) \u306e\u7d44\u306e\u6570\u3092\u8003\u3048\u308b.
    \r\n\\(m \\ ( 2 \\leqq m \\leqq 6 )\\) \u306e\u5024\u306b\u5bfe\u3057\u3066, \\((l,n)\\) \u306e\u7d44\u306f \\(\\textstyle\\sum\\limits _ {k=2}^{m} k-1\\) \u7d44\u3042\u308b\u306e\u3067, [2] \u3092\u307f\u305f\u3059 \\(( l, m, n )\\) \u306e\u7d44\u306f\r\n\\[\\begin{align}\r\n\\textstyle\\sum\\limits _ {m=2}^{6} \\textstyle\\sum\\limits _ {k=2}^{m}(k-1) & = \\textstyle\\sum\\limits _ {m=2}^{6} \\dfrac{m (m-1)}{2} \\\\\r\n& =1+3+6+10+15 \\\\\r\n& =35 \\quad \\text{\u7d44}\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n1 -\\dfrac{35}{6^3} = \\underline{\\dfrac{181}{216}}\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(1\\) \u500b\u306e\u3055\u3044\u3053\u308d\u3092 \\(3\\) \u56de\u7d9a\u3051\u3066\u6295\u3052\u308b\u3068\u304d, \\(1\\) \u56de\u76ee\u306b\u51fa\u308b\u76ee\u3092 \\(l\\) , \\(2\\) \u56de\u76ee\u306b\u51fa\u308b\u76ee\u3092 \\(m\\) , \\(3\\) \u56de\u76ee\u306b\u51fa\u308b\u76ee\u3092 \\(n\\) \u3067\u8868\u3059\u3053\u3068\u306b\u3059\u308b. \u3053\u306e\u3068\u304d, … \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":[60],"tags":[142,68],"class_list":["post-393","post","type-post","status-publish","format-standard","hentry","category-osaka_r_2012","tag-osaka_r","tag-68"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/393","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=393"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/393\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=393"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=393"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=393"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}