Question

(10.3.05) The function plotted below is f(x)2whenand zero otherwise. This function can be approximated on the interval [-1,1] by the function (a) Find the values of an, αι, α2, α3, and α4 using the integrals given in class. (Hint 1: Use the symmetry of f(x) so that you only need to integrate over positive values of x. Hint 2: To evaluate an for n 1,2,3,4, do the integration without plugging in n. Once you have done the integral and simplified the results, you can plug in the different values of n.) (b) Plot f(x) and Fx) on the same graph. I encourage using software such as Excel or Mathematica to do this. (c) If your plot of F(x) looks nothing like the triangle shape I have plotted below, you probably have not computed the a's correctly. If this is the case, find the error in your computation of the a's and try the plot again. YOU WILL RECEIVE NO CREDIT FOR THIS IF (a) You do not obtain a plot which reasonably reproduces the triangle shape shown. (b) You produce a shape that looks like the triangle shown, but the plot is unsupported by a clear and mostly correct computation of the 10. a's. This problem will be worth 20 points towards your homework grade instead of the normal 0.6 0.4 0.2 -1 0.5 0.5

Fourier Series

Answer 1

Solution :

Given that

" Let, f(x) = 1 - 2(x) ln = 1/lintegralf(x0 cos n pix/l dx: for n = 0 do = 1/lintegrall_-l f(x) dx for, f(x) = 1 - 2