{"id":26,"date":"2004-05-16T19:28:04","date_gmt":"2004-05-16T19:28:04","guid":{"rendered":"http:\/\/www.sixthform.info\/maths\/?p=26"},"modified":"2007-10-31T14:53:37","modified_gmt":"2007-10-31T14:53:37","slug":"nice-problem-2","status":"publish","type":"post","link":"https:\/\/www.sixthform.info\/maths\/?p=26","title":{"rendered":"Nice Problem"},"content":{"rendered":"<p>There&#8217;s a very nice problem on <a href=\"http:\/\/www.mathsoc.warwick.ac.uk\" target=\"_blank\">The University of Warwick Mathematical Society&#8217;s site<\/a>.<br \/>\nI won&#8217;t say exactly where because it has the solution there as well \ud83d\ude15 <\/p>\n<ol type=a>\n<li>If <img src='\/maths\/latexrender\/pictures\/8fa14cdd754f91cc6554c9e71929cce7.gif' title='f' alt='f' align=absmiddle> is continuously differentiable on the open interval <img src='\/maths\/latexrender\/pictures\/2d05e1f15387f87456155cd96cc06235.gif' title='(a,b)' alt='(a,b)' align=absmiddle>\n<li><img src='\/maths\/latexrender\/pictures\/b85ac5b0dde80aef85ede65e2edcbc28.gif' title='\\lim_{x \\to a^{+}}f(x)=\\infty' alt='\\lim_{x \\to a^{+}}f(x)=\\infty' align=absmiddle><\/li>\n<p><\/p>\n<li><img src='\/maths\/latexrender\/pictures\/552c8bb1816691f0da7103943749405c.gif' title='\\lim_{x \\to b^{-}}f(x)=-\\infty' alt='\\lim_{x \\to b^{-}}f(x)=-\\infty' align=absmiddle><\/li>\n<p><\/p>\n<li><img src='\/maths\/latexrender\/pictures\/75e4bc96e06977442c69fb726cdab42a.gif' title='f^{\\prime}(x)+f(x)^2 \\geq 1' alt='f^{\\prime}(x)+f(x)^2 \\geq 1' align=absmiddle><\/li>\n<\/li>\n<\/ol>\n<p>then prove that <img src='\/maths\/latexrender\/pictures\/1bcd533626298d345137ff8bad36f435.gif' title='b-a \\geq \\pi' alt='b-a \\geq \\pi' align=absmiddle><\/p>\n<p>Stuck!. Then click on <i>read more<\/i> for a hint<br \/>\n<!--more--><br \/>\nDefine <img src='\/maths\/latexrender\/pictures\/59b6c91c596ad0e670fd4e53ad2e2e45.gif' title='g(x)=\\tan^{-1}f(x)+x' alt='g(x)=\\tan^{-1}f(x)+x' align=absmiddle> for <img src='\/maths\/latexrender\/pictures\/d9a228a685dd5c1f9f4c32e048440c59.gif' title='x \\in (a,b)' alt='x \\in (a,b)' align=absmiddle><br \/>\nLook at [Unparseable or potentially dangerous latex formula. Error 4 ]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>There&#8217;s a very nice problem on The University of Warwick Mathematical Society&#8217;s site. I won&#8217;t say exactly where because it has the solution there as well \ud83d\ude15 If is continuously differentiable on the open interval then prove that Stuck!. Then click on read more for a hint<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-26","post","type-post","status-publish","format-standard","hentry","category-articles"],"_links":{"self":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/26","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=26"}],"version-history":[{"count":0,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/26\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}