{"id":789,"date":"2013-05-10T22:56:17","date_gmt":"2013-05-10T13:56:17","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=789"},"modified":"2021-03-23T17:17:54","modified_gmt":"2021-03-23T08:17:54","slug":"kyr201305","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr201305\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb2013\uff1a\u7b2c5\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(xy\\) \u5e73\u9762\u5185\u3067, \\(y\\) \u8ef8\u4e0a\u306e\u70b9 P \u3092\u4e2d\u5fc3\u3068\u3059\u308b\u5186 \\(C\\) \u304c \\(2\\) \u3064\u306e\u66f2\u7dda\r\n\\[\r\nC _ 1 : \\ y = \\sqrt{3} \\log (1+x) , \\quad C _ 2 \uff1a \\ y = \\sqrt{3} \\log (1-x)\r\n\\]\r\n\u3068\u305d\u308c\u305e\u308c\u70b9 A , \u70b9 B \u3067\u63a5\u3057\u3066\u3044\u308b\u3068\u3059\u308b.\r\n\u3055\u3089\u306b \u25b3PAB \u306f A \u3068 B \u304c \\(y\\) \u8ef8\u306b\u95a2\u3057\u3066\u5bfe\u79f0\u306a\u4f4d\u7f6e\u306b\u3042\u308b\u6b63\u4e09\u89d2\u5f62\u3067\u3042\u308b\u3068\u3059\u308b.\r\n\u3053\u306e\u3068\u304d \\(3\\) \u3064\u306e\u66f2\u7dda \\(C , C _ 1 , C _ 2\\) \u3067\u56f2\u307e\u308c\u305f\u90e8\u5206\u306e\u9762\u7a4d\u3092\u6c42\u3081\u3088.<\/p>\r\n<hr>\r\n<!--more-->\r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/kyoto_r_2013_05_01.png\" alt=\"kyoto_r_2013_05_01\" class=\"aligncenter size-full\" \/>\r\n<p>\u70b9 A \u306e \\(x\\) \u5ea7\u6a19\u3092 \\(t\\) \u3068\u3059\u308b.<br \/>\r\n\\(C _ 1\\) \u306e\u5f0f\u3092\u5fae\u5206\u3059\u308b\u3068\r\n\\[\r\ny' = \\dfrac{\\sqrt{3}}{1+x}\r\n\\]\r\n\u76f4\u7dda AP \u306f, \u70b9 A \u306b\u304a\u3051\u308b\u66f2\u7dda \\(C _ 1\\) \u306e\u6cd5\u7dda\u3067\u3042\u308a,\r\n\u25b3PAB \u304c\u6b63\u4e09\u89d2\u5f62\u3067\u3042\u308c\u3070, \u50be\u304d\u306f \\(-\\sqrt{3}\\) \u3067\u3042\u308b\u304b\u3089\r\n\\[\\begin{align}\r\n-\\dfrac{1+t}{\\sqrt{3}} & = -\\sqrt{3} \\\\\r\n\\text{\u2234} \\quad t & = 2\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, A \\(\\left( 2 , \\sqrt{3} \\log 3 \\right)\\) \u3067\u3042\u308a, \u25b3PAB \u306e \\(1\\) \u8fba\u306e\u9577\u3055\u306f \\(4\\) \u3067\u3042\u308b.<br \/>\r\n\u3053\u3053\u3067, \\(C _ 1\\) \u3092 \\(y\\) \u306e\u95a2\u6570\u3068\u307f\u306a\u3059\u3068\r\n\\[\\begin{align}\r\n\\dfrac{y}{\\sqrt{3}} & = \\log (1+x) \\\\\r\n\\text{\u2234} \\quad x & = e^{\\frac{y}{\\sqrt{3}}} -1\r\n\\end{align}\\]\r\n\u3053\u308c\u3089\u3068, \u56f3\u5f62\u304c \\(y\\) \u8ef8\u306b\u3064\u3044\u3066\u5bfe\u79f0\u3067\u3042\u308b\u3053\u3068\u306b\u7740\u76ee\u3059\u308c\u3070, \u6c42\u3081\u308b\u9762\u7a4d \\(S\\) \u306f\r\n\\[\\begin{align}\r\nS & = 2 \\left\\{ \\displaystyle\\int _ 0^{\\sqrt{3} \\log 3} \\left( e^{\\frac{y}{\\sqrt{3}}} -1 \\right) \\, dy \\right. \\\\\r\n& \\qquad \\left. -\\left( \\dfrac{1}{2} \\cdot 4^2 \\cdot \\dfrac{\\pi}{6} -\\dfrac{1}{2} \\cdot 2 \\sqrt{3} \\cdot 2 \\right) \\right\\} \\\\\r\n& = 2 \\left[ \\sqrt{3} e^{\\frac{y}{\\sqrt{3}}} -y \\right] _ 0^{\\sqrt{3} \\log 3} \\\\\r\n& \\qquad -2 \\left( \\dfrac{4 \\pi}{3} -2 \\sqrt{3}\\right) \\\\\r\n& = 2 \\left( 3 \\sqrt{3} -\\sqrt{3} \\log 3 -\\sqrt{3} \\right) \\\\\r\n& \\qquad -\\dfrac{8 \\pi}{3} +4 \\sqrt{3} \\\\\r\n& = \\underline{8 \\sqrt{3} -2 \\sqrt{3} \\log 3 -\\dfrac{8 \\pi}{3}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(xy\\) \u5e73\u9762\u5185\u3067, \\(y\\) \u8ef8\u4e0a\u306e\u70b9 P \u3092\u4e2d\u5fc3\u3068\u3059\u308b\u5186 \\(C\\) \u304c \\(2\\) \u3064\u306e\u66f2\u7dda \\[ C _ 1 : \\ y = \\sqrt{3} \\log (1+x) , \\quad C _ 2 \uff1a \\ y  &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kyr201305\/\">\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":[88],"tags":[140,111],"class_list":["post-789","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2013","tag-kyoto_r","tag-111"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/789","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=789"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/789\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=789"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=789"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=789"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}