{"id":48,"date":"2011-11-26T18:11:25","date_gmt":"2011-11-26T09:11:25","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=48"},"modified":"2021-10-09T04:03:28","modified_gmt":"2021-10-08T19:03:28","slug":"ngr201101","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ngr201101\/","title":{"rendered":"\u540d\u53e4\u5c4b\u5927\u7406\u7cfb2011\uff1a\u7b2c1\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(-\\dfrac{1}{4} \\lt s \\lt \\dfrac{1}{3}\\) \u3068\u3059\u308b. \\(xyz\\) \u7a7a\u9593\u5185\u306e\u5e73\u9762 \\(z = 0\\) \u306e\u4e0a\u306b\u9577\u65b9\u5f62\r\n\\[\r\nR _ s = \\left\\{ ( x , y , 0 ) | 1 \\leqq x \\leqq 2+4s , 1 \\leqq y \\leqq 2-3s \\right\\}\r\n\\]\r\n\u304c\u3042\u308b. \u9577\u65b9\u5f62 \\(R _ s\\) \u3092 \\(x\\) \u8ef8\u306e\u307e\u308f\u308a\u306b \\(1\\) \u56de\u8ee2\u3057\u3066\u3067\u304d\u308b\u7acb\u4f53\u3092 \\(K _ s\\) \u3068\u3059\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\u7acb\u4f53 \\(K _ s\\) \u306e\u4f53\u7a4d \\(V(s)\\) \u304c\u6700\u5927\u3068\u306a\u308b\u3068\u304d\u306e \\(s\\) \u306e\u5024, \u304a\u3088\u3073\u305d\u306e\u3068\u304d\u306e \\(V(s)\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(s\\) \u3092 <strong>(1)<\/strong> \u3067\u6c42\u3081\u305f\u5024\u3068\u3059\u308b. \u3053\u306e\u3068\u304d\u306e\u7acb\u4f53 \\(K _ s\\) \u3092 \\(y\\) \u8ef8\u306e\u307e\u308f\u308a\u306b \\(1\\) \u56de\u8ee2\u3057\u3066\u3067\u304d\u308b\u7acb\u4f53 \\(L\\) \u306e\u4f53\u7a4d\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n\r\n    <div id='extLink48'>\r\n        <p>\r\n            <a href='https:\/\/www.roundown.net\/nyushi\/ngr201101\/' name='ext48' onclick=\"showHide(48,'https:\/\/www.roundown.net\/nyushi\/ngr201101\/',this,'entry');return false;\">\u89e3\u7b54\u306f\u3053\u3061\u3089 &#187;<\/a>\r\n        <\/p>\r\n    <\/div>\r\n    <div id='extText48' style='display: none'>\r\n        \r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\\(-\\dfrac{1}{4} \\lt s \\lt \\dfrac{1}{3} \\quad ... [1]\\) \u306e\u3068\u304d, \\(R _ s\\) \u306f\u4e0b\u56f3\u659c\u7dda\u90e8\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/nagoya_r_201101_01.png\" alt=\"\" title=\"nagoya_r_201101_01\" class=\"aligncenter size-full\" \/>\r\n<p>\\[\\begin{align}\r\nV(s) & = \\pi \\left\\{ (2-3s)^2 -1^2 \\right\\} (1+4s) \\\\\r\n& = 3 \\pi ( 3s^2-4s+1 )( 4s+1 ) \\\\\r\n& = 3 \\pi ( \\underline{12s^3-13s+1} )\r\n\\end{align}\\]\r\n\u4e0b\u7dda\u90e8\u3092 \\(f(s)\\) \u3068\u304a\u304f\u3068\r\n\\[\r\nf'(s) = 36s^2-26s = 2s( 18s-13 )\r\n\\]\r\n[1] \u306e\u7bc4\u56f2\u3067 \\(f'(s)=0\\) \u3092\u3068\u304f\u3068\r\n\\[\r\ns=0\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(f(s)\\) \u306e\u5897\u6e1b\u8868\u306f\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a,\r\n\\[\r\n\\begin{array}{c|ccccc} s & -\\dfrac{1}{4} & \\cdots & 0 & \\cdots & \\dfrac{1}{3} \\\\ \\hline\r\nf'(s) & & + & 0 & 1 & \\\\ \\hline f(s) & & \\searrow & \\text{\u6700\u5927} & \\nearrow & \\end{array}\r\n\\]\r\n\u6700\u5927\u5024\u306f\r\n\\[\r\nf(0) = 1\r\n\\]\r\n\u3088\u3063\u3066 \\(V(s)\\) \u306f, \\(s = \\underline{0}\\) \u306e\u3068\u304d\u6700\u5927\u3068\u306a\u308a, \\(V(0) =\\underline{3 \\pi}\\) .<\/p>\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\\(K _ 0\\) \u306f \\(xz\\) \u5e73\u9762\u306b\u3064\u3044\u3066\u5bfe\u79f0\u306a\u306e\u3067, \\(y \\gt 0\\) \u306e\u90e8\u5206\u306b\u3064\u3044\u3066\u8003\u3048\u308b.<br \/>\r\n\\(K _ 0\\) \u3092 \\(x\\) \u8ef8\u65b9\u5411\u304b\u3089\u898b\u308b\u3068\u53f3\u56f3\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n<p><img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/nagoya_r_201101_02.png\" alt=\"\" title=\"nagoya_r_201101_02\" class=\"aligncenter size-full\" \/><\/p>\r\n<p>\\(K _ 0\\) \u306e\u5e73\u9762 \\(y = t \\ ( 0 \\leqq t \\leqq 2 )\\) \u306b\u3088\u308b\u65ad\u9762\u56f3\u304b\u3089, \\(L\\) \u306e\u65ad\u9762\u7a4d\u3092\u6c42\u3081\u3066\u3044\u304f.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(1 \\leqq t \\leqq 2\\) \u306e\u3068\u304d<br \/>\r\n\\(K _ 0\\) \u306e\u65ad\u9762\u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b.\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/nagoya_r_201101_03.png\" alt=\"\" title=\"nagoya_r_201101_03\" class=\"aligncenter size-full\" \/>\r\n\\[\\begin{align}\r\n\\text{OA} & = \\sqrt{(4-t^2)+2^2} = \\sqrt{8-t^2} , \\\\\r\n\\text{OB} & = 1\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(L\\) \u306e\u65ad\u9762\u7a4d \\(T(t)\\) \u306f\r\n\\[\r\nT(t)= ( \\text{OA}^2-\\text{OB}^2 ) \\pi = (7-t^2) \\pi\r\n\\]<\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(0 \\leqq t \\leqq 1\\) \u306e\u3068\u304d<br \/>\r\n\\(K _ 0\\) \u306e\u65ad\u9762\u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b.\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/nagoya_r_201101_04.png\" alt=\"\" title=\"nagoya_r_201101_04\" class=\"aligncenter size-full\" \/>\r\n\\[\\begin{align}\r\n\\text{OC} & = \\sqrt{(4-t^2)+2^2} = \\sqrt{8-t^2} , \\\\\r\n\\text{OD} & = \\sqrt{(1-t^2)+1^2} = \\sqrt{2-t^2}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(L\\) \u306e\u65ad\u9762\u7a4d \\(T(t)\\) \u306f\r\n\\[\r\nT(t) = ( \\text{OA}^2-\\text{OB}^2 ) \\pi = 6 \\pi\r\n\\]<\/li>\r\n<\/ol>\r\n<p><strong>1*<\/strong> <strong>2*<\/strong> \u3088\u308a\u6c42\u3081\u308b\u4f53\u7a4d \\(W\\) \u306f\r\n\\[\\begin{align}\r\nW & = 2 \\left\\{ 6 \\pi \\cdot 1 +\\displaystyle\\int _ 1^2 (7-t^2) \\pi \\, dt \\right\\} \\\\\r\n& = 12 \\pi +14 \\pi - 2\\pi \\left[ \\dfrac{t^3}{3} \\right] _ 1^2 \\\\\r\n& = \\left( 26-\\dfrac{14}{3} \\right) \\pi =\\underline{\\dfrac{64 \\pi}{3}}\r\n\\end{align}\\]\r\n\r\n        <p>\r\n            <a href='#ext48' onclick=\"showHide(48,0,this,'entry');return true;\">&#171; \u89e3\u7b54\u3092\u96a0\u3059 <\/a>\r\n        <\/p>\r\n    <\/div>","protected":false},"excerpt":{"rendered":"\\(-\\dfrac{1}{4} \\lt s \\lt \\dfrac{1}{3}\\) \u3068\u3059\u308b. \\(xyz\\) \u7a7a\u9593\u5185\u306e\u5e73\u9762 \\(z = 0\\) \u306e\u4e0a\u306b\u9577\u65b9\u5f62 \\[ R _ s = \\left\\{ ( x , y , 0 ) [&hellip;]","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":[35],"tags":[143,13],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/48"}],"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=48"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/48\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=48"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=48"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=48"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}