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.
T4(x) =
(b) Use Taylor's Inequality to estimate the accuracy of the approximation
f(x) ≈ Tn(x) when x lies in the given interval. (Round your answer to four decimal places.)
|R4(x)| ≤
(c) Check your result in part (b) by graphing |Rn(x)|.