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 November 12th, 2009, 12:29 PM #1 Newbie   Joined: Nov 2009 Posts: 1 Thanks: 0 Taylor series & trigonometric functions Hello everyone, Im working on some homework atm, and Im unsure about this question: Find the first three terms of the Taylor's series for sin(x^{2}) . Using this approximation to estimate the integral - its the integral from 3 to 0, of the function sin(x^2). I know how to do the taylor series but when im entering the my answer, the web app says its wrong. Is the first term, f(a) at zero not cos(0)? Then I figured that if they're asking for the taylor series of an integral, then the derivative of a functions integral is that function, so I tried entering sin(3) but its still wrong. Any help here would be appreciated thanks...
 November 12th, 2009, 01:36 PM #2 Senior Member   Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0 The Taylor series of $\sin\,y$ around 0 is $\sin y=\sin(0)+y\sin'(0)+\frac{y^2}{2!}\sin'#3 9;(0)+\frac{y^3}{3!}\sin^{(3)}(0)+\frac{y^4}{4!}\s in^{(4)}(0)+\frac{y^5}{5!}\sin^{(5)}(0)+\mathcal{O }(y^6).$ Plug in the derivatives, and set $y=x^2.$

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