Consider the following function.

f(x) = x sin(x), a = 0, n = 4, 0.5 x 0.5

(a)Approximate f by a Taylor polynomial with degree n at the number a.

Consider the following function. f(x) = x sin(x), a =0, n = 4, -0.5 x$ 0.5 (a) Approximate f by a Taylor polynomial with degree n at the number a. TA( x) = x- (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) & T,(x) when x lies in the given interval. (Round your answer to four decimal places.) IRA(x)| S .0007385 (c) Check your result in part (b) by graphing IR,, (x) 1. J 0.09020 y 0.00020 -0.4 X -0.2 0.2 0.4 X -0.4 -0.2 0.2 0.00015 0.4 0.00015 -0.00005 -0.00905 0.00010 -0.00010 0.0010 -0.0010 0.00005 0.00005 -0.00015 -0.09015 -0.00020 -0.4 -0.2 X O -0.4 -0.2 0.2 0.2 0.4 0.4 AO -0.00020