{"id":1989,"date":"2021-11-21T15:59:01","date_gmt":"2021-11-21T06:59:01","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1989"},"modified":"2021-11-21T15:59:01","modified_gmt":"2021-11-21T06:59:01","slug":"osr202105","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/osr202105\/","title":{"rendered":"\u962a\u5927\u7406\u7cfb2021\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(a\\) \u3092\u5b9f\u6570\u3068\u3059\u308b.\r\n\\(x\\) \u306b\u3064\u3044\u3066\u306e\u65b9\u7a0b\u5f0f \\(x -\\tan x = a\\) \u306e\u5b9f\u6570\u89e3\u306e\u3046\u3061,\r\n\\(|x| \\lt \\dfrac{\\pi}{2}\\) \u3092\u307f\u305f\u3059\u3082\u306e\u304c\u3061\u3087\u3046\u3069\\(1\\) \u3064\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u81ea\u7136\u6570 \\(n\\) \u306b\u5bfe\u3057, \\(x -\\tan x = n \\pi\\) \u304b\u3064 \\(|x| \\lt \\dfrac{\\pi}{2}\\) \u3092\u307f\u305f\u3059\u5b9f\u6570 \\(x\\) \u3092 \\(x_n\\) \u3068\u304a\u304f.\r\n\u3053\u306e\u3068\u304d, \u66f2\u7dda \\(C : y = \\sin x\\) \u4e0a\u306e\u70b9 P \\(( t , \\sin t)\\) \u306b\u304a\u3051\u308b\u63a5\u7dda\u304c,\r\n\u4e0d\u7b49\u5f0f \\(x \\geqq \\dfrac{\\pi}{2}\\) \u306e\u8868\u3059\u9818\u57df\u306b\u542b\u307e\u308c\u308b\u70b9\u306b\u304a\u3044\u3066\u3082\u66f2\u7dda \\(C\\) \u3068\u63a5\u3059\u308b\u305f\u3081\u306e\u5fc5\u8981\u5341\u5206\u6761\u4ef6\u306f,\r\n\\(t\\) \u304c \\(x_1 , x_2 , x_3 , \\cdots\\) \u306e\u3044\u305a\u308c\u304b\u3068\u7b49\u3057\u3044\u3053\u3068\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/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) = x -\\tan x\\) \u3068\u304a\u304f\u3068\r\n\\[\r\nf'(x) = 1 -\\dfrac{1}{\\cos^2 x} = -\\tan^2 x \\leqq 0\r\n\\]\r\n\u3086\u3048\u306b, \\(f(x)\\) \u306f\u5358\u8abf\u6e1b\u5c11\u3057, \u3055\u3089\u306b\r\n\\[\r\n\\displaystyle\\lim_{x \\rightarrow -\\frac{\\pi}{2}} f(x) = \\infty \\ , \\ \\displaystyle\\lim_{x \\rightarrow \\frac{\\pi}{2}} f(x) = -\\infty\r\n\\]\r\n\u306a\u306e\u3067, \\(f(x) = a\\) \u3092\u307f\u305f\u3059\u5b9f\u6570\u89e3\u304c\u305f\u3060 \\(1\\) \u3064\u5b58\u5728\u3059\u308b.<\/p>\r\n

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

    (1)<\/strong> \u306e\u7d50\u679c\u3088\u308a, \\(f(x) = n \\pi\\) \u3092\u307f\u305f\u3059\u5b9f\u6570\u89e3 \\(x_n\\) \u304c\u305f\u3060 \\(1\\) \u3064\u5b58\u5728\u3059\u308b.
    \r\n\\(C\\) \u306e\u5f0f\u3088\u308a, \\(y' = \\cos x\\) \u306a\u306e\u3067, P \u306b\u304a\u3051\u308b\u63a5\u7dda\u306e\u5f0f\u306f\r\n\\[\r\ny = (x-t) \\cos t +\\sin t = x \\cos t -t \\cos t +\\sin t\r\n\\]\r\n\u3053\u308c\u304c\u70b9 \\(( p , \\sin p ) \\ \\left( p \\geqq \\dfrac{\\pi}{2} \\right)\\) \u306e\u63a5\u7dda\u306b\u3082\u306a\u308b\u306e\u306f\r\n\\[\r\n\\left\\{ \\begin{array}{ll} \\cos p = \\cos t & ... [1] \\\\ -p \\cos p +\\sin p = -t \\cos t +\\sin t & ... [2] \\end{array} \\right.\r\n\\]\r\n\u304c\u6210\u7acb\u3059\u308b\u3068\u304d.
    \r\n[1] \u3088\u308a\r\n\\[\r\np = 2n \\pi \\pm t \\quad ( \\ n \\text{\u306f\u6b63\u306e\u6574\u6570} \\ )\r\n\\]\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(p = 2n \\pi +t\\) \u306e\u3068\u304d
      \r\n[2] \u306b\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n-( 2n \\pi +t ) \\cos t +\\sin t & = -t \\cos t +\\sin t \\\\\r\n2n \\pi \\cos t & = 0\r\n\\end{align}\\]\r\n\\(\\cos t \\neq 0\\) \u306a\u306e\u3067, \u3053\u308c\u3092\u307f\u305f\u3059 \\(t\\) \u306f\u5b58\u5728\u3057\u306a\u3044.<\/p><\/li>\r\n

    2. 2*<\/strong>\u3000\\(p = 2n \\pi -t\\) \u306e\u3068\u304d
      \r\n[2] \u306b\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n-( 2n \\pi -t ) \\cos t -\\sin t & = -t \\cos t +\\sin t \\\\\r\n2 (n \\pi -t ) \\cos t & = 2 \\sin t \\\\\r\nt -\\tan t & = n \\pi \\quad \\quad ( \\text{\u2235} \\ \\cos t \\neq 0 \\ )\\\\\r\n\\text{\u2234} \\quad t & = x_n\r\n\\end{align}\\]<\/li>\r\n<\/ol>\r\n

      1*<\/strong> 2*<\/strong> \u3088\u308a, [1] [2] \u304c\u6210\u7acb\u3059\u308b\u306a\u3089\u3070, \\(t = x_n\\) .
      \r\n\u9006\u306b, \\(t = x_n\\) \u306a\u3089\u3070, \\(p = 2n \\pi -x _ n \\geqq \\dfrac{\\pi}{2}\\) \u304c [1] [2] \u3092\u307f\u305f\u3059.
      \r\n\u3088\u3063\u3066, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\\(a\\) \u3092\u5b9f\u6570\u3068\u3059\u308b. \\(x\\) \u306b\u3064\u3044\u3066\u306e\u65b9\u7a0b\u5f0f \\(x -\\tan x = a\\) \u306e\u5b9f\u6570\u89e3\u306e\u3046\u3061, \\(|x| \\lt \\dfrac{\\pi}{2}\\) \u3092\u307f\u305f\u3059\u3082\u306e\u304c\u3061\u3087\u3046\u3069\\( … \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":[172],"tags":[142,165],"class_list":["post-1989","post","type-post","status-publish","format-standard","hentry","category-osaka_r_2021","tag-osaka_r","tag-165"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1989","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=1989"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1989\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1989"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1989"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1989"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}