{"id":1388,"date":"2017-02-25T01:22:07","date_gmt":"2017-02-24T16:22:07","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1388"},"modified":"2021-03-18T16:16:04","modified_gmt":"2021-03-18T07:16:04","slug":"kyr201604","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr201604\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb2016\uff1a\u7b2c4\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(xyz\\) \u7a7a\u9593\u306b\u304a\u3044\u3066, \u5e73\u9762 \\(y=z\\) \u306e\u4e2d\u3067\r\n\\[\r\n|x| \\leqq \\dfrac{e^y +e^{-y}}{2} -1 , \\quad 0 \\leqq y \\leqq \\log a\r\n\\]\r\n\u3067\u4e0e\u3048\u3089\u308c\u308b\u56f3\u5f62 \\(D\\) \u3092\u8003\u3048\u308b. \u305f\u3060\u3057 \\(a\\) \u306f \\(1\\) \u3088\u308a\u5927\u304d\u3044\u5b9a\u6570\u3068\u3059\u308b.<br \/>\r\n\u3000\u3053\u306e\u56f3\u5f62 \\(D\\) \u3092 \\(y\\) \u8ef8\u306e\u307e\u308f\u308a\u306b \\(1\\) \u56de\u8ee2\u3055\u305b\u3066\u3067\u304d\u308b\u7acb\u4f53\u306e\u4f53\u7a4d\u3092\u6c42\u3081\u3088.<\/p>\r\n<hr\/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>\\(f(t) = \\dfrac{e^t +e^{-t}}{2} -1\\) \u3068\u304a\u304f.<br \/>\r\n\u56f3\u5f62 \\(D\\) \u306e\u5e73\u9762 \\(y = t \\ \\left( 0 \\leqq t \\leqq \\log a \\right)\\) \u3067\u306e\u5207\u308a\u53e3\u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/kyr20160401.svg\" alt=\"\" class=\"aligncenter size-full\" \/>\r\n<p>\u3053\u308c\u3092 \\(y\\) \u8ef8\u306e\u307e\u308f\u308a\u306b\u56de\u8ee2\u3059\u308b\u3068, \u30c9\u30fc\u30ca\u30c4\u578b\u306e\u9818\u57df\u3092\u63cf\u304d, \u5185\u5074, \u5916\u5074\u306e\u5186\u306e\u534a\u5f84\u3092\u305d\u308c\u305e\u308c \\(r _ t , R _ t\\) \u3068\u304a\u3051\u3070\r\n\\[\\begin{align}\r\n{r _ t}^2 & = t^2 , \\\\\r\n{R _ t}^2 & = t^2 +\\left\\{ f(t) \\right\\}^2\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u9818\u57df\u306e\u9762\u7a4d \\(S(t)\\) \u306f\r\n\\[\r\nS(t) = \\pi {R _ t}^2 -\\pi {r _ t}^2 = \\pi \\left\\{ f(t) \\right\\}^2\r\n\\]\r\n\u3053\u3053\u3067\r\n\\[\\begin{align}\r\n\\left\\{ f(t) \\right\\}^2 & = \\dfrac{\\left( e^t +e^{-t} \\right)^2}{4} -\\left( e^t +e^{-t} \\right) +1 \\\\\r\n& = \\dfrac{e^{2t}}{4} +\\dfrac{e^{-2t}}{4} -e^t -e^{-t} +\\dfrac{3}{2}\r\n\\end{align}\\]\r\n\u306a\u306e\u3067, \u6c42\u3081\u308b\u4f53\u7a4d \\(V\\) \u306f\r\n\\[\\begin{align}\r\nV & = \\pi \\displaystyle\\int _ {0}^{\\log a} \\left\\{ f(t) \\right\\}^2 \\, dt \\\\\r\n& = \\pi \\left[ \\dfrac{e^{2t}}{8} -\\dfrac{e^{-2t}}{8} -e^t +e^{-t} +\\dfrac{3t}{2} \\right] _ {0}^{\\log a} \\\\\r\n& = \\underline{\\left( \\dfrac{e^2 -e^{-2}}{8} +e -e^{-1} +\\dfrac{3}{2} \\log a \\right) \\pi}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(xyz\\) \u7a7a\u9593\u306b\u304a\u3044\u3066, \u5e73\u9762 \\(y=z\\) \u306e\u4e2d\u3067 \\[ |x| \\leqq \\dfrac{e^y +e^{-y}}{2} -1 , \\quad 0 \\leqq y \\leqq \\log a \\] \u3067\u4e0e\u3048\u3089\u308c\u308b &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kyr201604\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/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":[151],"tags":[140,162],"class_list":["post-1388","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2016","tag-kyoto_r","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1388","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=1388"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1388\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1388"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1388"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1388"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}