{"id":2150,"date":"2025-03-14T23:56:56","date_gmt":"2025-03-14T14:56:56","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=2150"},"modified":"2025-03-16T21:13:41","modified_gmt":"2025-03-16T12:13:41","slug":"tkr2025","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkr2025\/","title":{"rendered":"\u6771\u5927\u7406\u7cfb2025\uff1a\u554f\u984c"},"content":{"rendered":"

\u7b2c 1 \u554f<\/h4>\r\n
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\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e\u70b9 A $( 0 , 0 )$ , B $( 0 , 1 )$ , C $( 1 , 1 )$ , D $( 1 , 0 )$ \u3092\u8003\u3048\u308b. \u5b9f\u6570 $0 \\lt t \\lt 1$ \u306b\u5bfe\u3057\u3066, \u7dda\u5206 AB , BC , CD \u3092 $t : (1-t)$ \u306b\u5185\u5206\u3059\u308b\u70b9\u3092\u305d\u308c\u305e\u308c $\\text{P}_t$ , $\\text{Q}_t$ , $\\text{R}_t$ \u3068\u3057, \u7dda\u5206 $\\text{P}_t \\text{Q}_t$ , $\\text{Q}_t \\text{R}_t$ \u3092 $t : (1-t)$ \u306b\u5185\u5206\u3059\u308b\u70b9\u3092\u305d\u308c\u305e\u308c $\\text{S}_t$ , $\\text{T}_t$ \u3068\u3059\u308b. \u3055\u3089\u306b, \u7dda\u5206 $\\text{S}_t \\text{T}_t$ \u3092 $t : (1-t)$ \u306b\u5185\u5206\u3059\u308b\u70b9\u3092 $\\text{U}_t$ \u3068\u3059\u308b. \u307e\u305f, \u70b9 A \u3092 $\\text{U}_0$ , \u70b9 D \u3092 $\\text{U}_1$ \u3068\u3059\u308b. <\/p>\r\n

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  1. (1)<\/strong>\u3000\u70b9 $\\text{U}_t$ \u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088. <\/li>\r\n
  2. (2)<\/strong>\u3000$t$ \u304c $0 \\leqq t \\leqq 1$ \u306e\u7bc4\u56f2\u3092\u52d5\u304f\u3068\u304d\u306b\u70b9 $\\text{U}_t$ \u306e\u63cf\u304f\u66f2\u7dda\u3068, \u7dda\u5206 AD \u3067\u56f2\u307e\u308c\u305f\u90e8\u5206\u306e\u9762\u7a4d\u3092\u6c42\u3081\u3088. <\/li>\r\n
  3. (3)<\/strong>\u3000$a$ \u304c $0 \\lt a \\lt 1$ \u3092\u6e80\u305f\u3059\u5b9f\u6570\u3068\u3059\u308b. $t$ \u304c $0 \\leqq t \\leqq a$ \u306e\u7bc4\u56f2\u3092\u52d5\u304f\u3068\u304d\u306b\u70b9 $\\text{U}_t$ \u306e\u63cf\u304f\u66f2\u7dda\u306e\u9577\u3055\u3092, $a$ \u306e\u591a\u9805\u5f0f\u306e\u5f62\u3067\u6c42\u3081\u3088. <\/li>\r\n<\/ol>\r\n
    \r\n

    \u7b2c 2 \u554f<\/h4>\r\n
    \r\n
      \r\n
    1. (1)<\/strong>\u3000$x \\gt 0$ \u306e\u3068\u304d, \u4e0d\u7b49\u5f0f $\\log x \\leqq x-1$ \u3092\u793a\u305b. <\/li>\r\n
    2. (2)<\/strong>\u3000\u6b21\u306e\u6975\u9650\u3092\u6c42\u3081\u3088.\r\n$$\\displaystyle\\lim_{n \\rightarrow \\infty} n \\displaystyle\\int_1^2 \\log \\left( \\dfrac{1 +x^{\\large\\frac{1}{n}}}{2} \\right) \\, dx$$<\/li>\r\n<\/ol>\r\n
      \r\n

      \u7b2c 3 \u554f<\/h4>\r\n
      \r\n

      \u5e73\u884c\u56db\u8fba\u5f62 ABCD \u306b\u304a\u3044\u3066, $\\angle \\text{ABC} = \\dfrac{\\pi}{6}$ , $\\text{AB} = a$ , $\\text{BC} = b$ , $a \\leqq b$ \u3068\u3059\u308b. \u6b21\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u9577\u65b9\u5f62 EFGH \u3092\u8003\u3048, \u305d\u306e\u9762\u7a4d\u3092 $S$ \u3068\u3059\u308b. <\/p>\r\n

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      1. \u6761\u4ef6\uff1a<\/strong>\u3000\u70b9 A , B , C , D \u306f\u305d\u308c\u305e\u308c\u8fba EF , FG , GH , HE \u4e0a\u306b\u3042\u308b. <\/li>\r\n<\/ol>\r\n

        \u305f\u3060\u3057, \u8fba\u306f\u305d\u306e\u4e21\u7aef\u306e\u70b9\u3082\u542b\u3080\u3082\u306e\u3068\u3059\u308b. <\/p>\r\n

          \r\n
        1. (1)<\/strong>\u3000$\\angle \\text{BCG} = \\theta$ \u3068\u3059\u308b\u3068\u304d, $S$ \u3092 $a , b, \\theta$ \u3092\u7528\u3044\u3066\u8868\u305b. <\/li>\r\n
        2. (2)<\/strong>\u3000$S$ \u306e\u3068\u308a\u3046\u308b\u5024\u306e\u6700\u5927\u5024\u3092 $a , b$ \u3092\u7528\u3044\u3066\u8868\u305b. <\/li>\r\n<\/ol>\r\n
          \r\n

          \u7b2c 4 \u554f<\/h4>\r\n
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          \u3053\u306e\u554f\u3044\u3067\u306f, $0$ \u4ee5\u4e0a\u306e\u6574\u6570\u306e $2$ \u4e57\u306b\u306a\u308b\u6570\u3092\u5e73\u65b9\u6570\u3068\u547c\u3076. $a$ \u3092\u6b63\u306e\u6574\u6570\u3068\u3057, $f_a (x) = x^2 +x -a$ \u3068\u304a\u304f. <\/p>\r\n

            \r\n
          1. (1)<\/strong>\u3000$n$ \u3092\u6b63\u306e\u6574\u6570\u3068\u3059\u308b. $f_a (n)$ \u304c\u5e73\u65b9\u6570\u306a\u3089\u3070, $n \\leqq a$ \u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b. <\/li>\r\n
          2. (2)<\/strong>\u3000$f_a (n)$ \u304c\u5e73\u65b9\u6570\u3068\u306a\u308b\u6b63\u306e\u6574\u6570 $n$ \u306e\u500b\u6570\u3092 $N_a$ \u3068\u304a\u304f. \u6b21\u306e\u6761\u4ef6 (i)<\/strong> , (ii)<\/strong> \u304c\u540c\u5024\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b. \r\n
              \r\n
            1. (i)<\/strong>\u3000$N_a = 1$ \u3067\u3042\u308b. <\/li>\r\n
            2. (ii)<\/strong>\u3000$4a +1$ \u306f\u7d20\u6570\u3067\u3042\u308b. <\/li>\r\n<\/ol><\/li>\r\n<\/ol>\r\n
              \r\n

              \u7b2c 5 \u554f<\/h4>\r\n
              \r\n

              $n$ \u3092 $2$ \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b. $1$ \u304b\u3089 $n$ \u307e\u3067\u306e\u6570\u5b57\u304c\u66f8\u304b\u308c\u305f\u672d\u304c\u5404 $1$ \u679a\u305a\u3064\u5408\u8a08 $n$ \u679a\u3042\u308a, \u6a2a\u4e00\u5217\u306b\u7f6e\u304b\u308c\u3066\u3044\u308b. $1$ \u4ee5\u4e0a $(n-1)$ \u4ee5\u4e0b\u306e\u6574\u6570 $i$ \u306b\u5bfe\u3057\u3066, \u6b21\u306e\u64cd\u4f5c $( \\text{T}_i )$ \u3092\u8003\u3048\u308b. <\/p>\r\n

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              1. $( \\text{T}_i )$\u3000\u5de6\u304b\u3089 $i$ \u756a\u76ee\u306e\u672d\u306e\u6570\u5b57\u304c, \u5de6\u304b\u3089 $(i+1)$ \u756a\u76ee\u306e\u672d\u306e\u6570\u5b57\u3088\u308a\u3082\u5927\u304d\u3051\u308c\u3070, \u3053\u308c\u3089 $2$ \u679a\u306e\u672d\u306e\u4f4d\u7f6e\u3092\u5165\u308c\u304b\u3048\u308b. \u305d\u3046\u3067\u306a\u3051\u308c\u3070, \u672d\u306e\u4f4d\u7f6e\u3092\u304b\u3048\u306a\u3044. <\/li>\r\n<\/ol>\r\n

                \u6700\u521d\u306e\u72b6\u614b\u306b\u304a\u3044\u3066\u672d\u306e\u6570\u5b57\u306f\u5de6\u304b\u3089 $A_1 , A_2 , \\cdots , A_n$ \u3067\u3042\u3063\u305f\u3068\u3059\u308b. \u3053\u306e\u72b6\u614b\u304b\u3089 $(n-1)$ \u56de\u306e\u64cd\u4f5c $( \\text{T}_1 , \\text{T}_2 , \\cdots , \\text{T}_{n-1} )$ \u3092\u9806\u306b\u884c\u3063\u305f\u5f8c, \u7d9a\u3051\u3066 $(n-1)$ \u56de\u306e\u64cd\u4f5c $( \\text{T}_{n-1} , \\cdots , \\text{T}_2 , \\text{T}_1 )$ \u3092\u9806\u306b\u884c\u3063\u305f\u3068\u3053\u308d, \u672d\u306e\u6570\u5b57\u306f\u5de6\u304b\u3089 $1 , 2 , \\cdots , n$ \u3068\u5c0f\u3055\u3044\u9806\u306b\u4e26\u3093\u3060. \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. <\/p>\r\n

                  \r\n
                1. (1)<\/strong>\u3000$A_1$ \u3068 $A_2$ \u306e\u3046\u3061\u5c11\u306a\u304f\u3068\u3082\u4e00\u65b9\u306f $2$ \u4ee5\u4e0b\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b. <\/li>\r\n
                2. (2)<\/strong>\u3000\u6700\u521d\u306e\u72b6\u614b\u3068\u3057\u3066\u3042\u308a\u3046\u308b\u672d\u306e\u6570\u5b57\u306e\u4e26\u3073\u65b9 $A_1 , A_2 , \\cdots , A_n$ \u306e\u7dcf\u6570\u3092 $c_n$ \u3068\u3059\u308b. $n$ \u304c $4$ \u4ee5\u4e0a\u306e\u6574\u6570\u3067\u3042\u308b\u3068\u304d, $c_n$ \u3092 $c_{n-1}$ \u3068 $c_{n-2}$ \u3092\u7528\u3044\u3066\u8868\u305b. <\/li>\r\n<\/ol>\r\n
                  \r\n

                  \u7b2c 6 \u554f<\/h4>\r\n
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                  \u8907\u7d20\u6570\u5e73\u9762\u4e0a\u306e\u70b9 $\\dfrac{1}{2}$ \u3092\u4e2d\u5fc3\u3068\u3059\u308b\u534a\u5f84 $\\dfrac{1}{2}$ \u306e\u5186\u306e\u5468\u304b\u3089\u539f\u70b9\u3092\u9664\u3044\u305f\u66f2\u7dda\u3092 $C$ \u3068\u3059\u308b. <\/p>\r\n

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                  1. (1)<\/strong>\u3000\u66f2\u7dda $C$ \u4e0a\u306e\u8907\u7d20\u6570 $z$ \u306b\u5bfe\u3057, $\\dfrac{1}{z}$ \u306e\u5b9f\u90e8\u306f $1$ \u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b. <\/li>\r\n
                  2. (2)<\/strong>\u3000$\\alpha , \\beta$ \u3092\u66f2\u7dda $C$ \u4e0a\u306e\u76f8\u7570\u306a\u308b\u8907\u7d20\u6570\u3068\u3059\u308b\u3068\u304d, $\\dfrac{1}{\\alpha^2} +\\dfrac{1}{\\beta^2}$ \u304c\u3068\u308a\u3046\u308b\u7bc4\u56f2\u3092\u8907\u7d20\u6570\u5e73\u9762\u4e0a\u306b\u56f3\u793a\u305b\u3088. <\/li>\r\n
                  3. (3)<\/strong>\u3000$\\gamma$ \u3092 (2)<\/strong> \u3067\u6c42\u3081\u305f\u7bc4\u56f2\u306b\u5c5e\u3055\u306a\u3044\u8907\u7d20\u6570\u3068\u3059\u308b\u3068\u304d, $\\dfrac{1}{\\gamma}$ \u306e\u5b9f\u90e8\u304c\u3068\u308a\u3046\u308b\u5024\u306e\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u3092\u6c42\u3081\u3088. <\/li>\r\n<\/ol>\r\n
                    ","protected":false},"excerpt":{"rendered":"\u7b2c 1 \u554f \u5ea7\u6a19\u5e73\u9762\u4e0a\u306e\u70b9 A $( 0 , 0 )$ , B $( 0 , 1 )$ , C $( 1 , 1 )$ , D $( 1 , 0 )$ \u3092\u8003\u3048\u308b. \u5b9f\u6570 $0 \\lt t \\lt 1$ \u306b\u5bfe\u3057\u3066, \u7dda\u5206 … \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":[209],"tags":[210],"class_list":["post-2150","post","type-post","status-publish","format-standard","hentry","category-tokyo_r_2025","tag-210"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2150","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=2150"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2150\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=2150"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=2150"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=2150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}