kingjewel1 Posted March 16, 2005 Share Posted March 16, 2005 Hi there guys! this one's interesting but got me stumped. How would i show that the values of x at which sinxe^(-sinx) has stationary points form an arithmetic sequence? Thanks! Link to comment Share on other sites More sharing options...
bloodhound Posted March 17, 2005 Share Posted March 17, 2005 i assume you meant [sinx][exp(-sinx)]. just do the most obvious thing which is to find its derivative. which comes out to be [cosx]exp[-sinx] - [sinx][cosx]exp[-sinx]. to find the stationary points , find points such that the derivative at the point is zero. so setting that to 0 we get [cosx]exp[-sinx] - [sinx][cosx]exp[-sinx] = 0 iff cosx - sinx[cosx] = 0 as the exponential is never 0. so we have either cosx = 0 or sinx = 1 which gives just the same arithmetic sequence of solutions namely (pi/2 + n*pi), where n ranges over the integers. Link to comment Share on other sites More sharing options...
kingjewel1 Posted March 17, 2005 Author Share Posted March 17, 2005 thanks for your help! Link to comment Share on other sites More sharing options...
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