HW1 - approximation of the rst derivative of the following...

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EMAE 250.100: Homework 1 January 13, 2011 1. [2pts] Derive Taylor series expansion for the following function from x i = 0: f ( x ) = e x . 2. For the following function: f ( x ) = sin x (a) [2pts] Derive zero to third order Taylor series approximation of x i +1 about a point x i = 0 . 9 with a step size h = x i +1 - x i = 0 . 1. (b) [2pts] Compute the true value of f ( x i +1 ) directly from the given function and find true relative errors for each approximation. Discuss the results. 3. For the following function: f ( x ) = - cos x (a) [2pts] Using the first forward finite divided difference method, compute the
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Unformatted text preview: approximation of the rst derivative of the following function at x i = 1 where the step size h = 0 . 1. Repeat the process for h = 0 . 05 and h = 0 . 01. (b) [2pts] Compute the true fractional relative error for each case by using the analytical solution of f ( x ) = sin x . Discuss the results. *You may use a calculator to obtain numerical values of sin x and cos x . 1...
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