Consider the following function and its power series:

a. Let S_n(x) be the sum of the first n terms of the series. With n = 5 and n = 10, graph f(x) and S_n(x) at the sample points x = -0.9, -0.8,  . . , -0.1, 0, 0.1,  . . , 0.8, 0.9 (two graphs). Where is the difference in the graphs the greatest?

b. What value of n is needed to guarantee that |f(x) - S_n(x) |< 0.01 at all of the sample points?

Transcribed Image Text:

1 Skx*-1, for –1 < x < 1. f(x) (1 – x)² k=1 ||