Find the fourth Taylor polynomial P4(x) for the function f (x) x(ex)2 about x0 0 a Find an upper bound for f (x) P4(x) , for 0 x 0 4 b Approximate c Find an upper bound for the error in (b) using d Approximate f '(0 2) using P '4(0 2), and find the error 04 f(x) dx usingP) dr 0 Pa)dx

Question: Find the fourth Taylor polynomial P4(x) for the function f (x) = x(ex)2 about x0 = 0. a. Find an upper bound for |f (x)

Find the fourth Taylor polynomial P4(x) for the function f (x) = x(ex)2 about x0 = 0.
a. Find an upper bound for |f (x) ˆ’ P4(x)|, for 0 ‰¤ x ‰¤ 0.4.
b. Approximate

c. Find an upper bound for the error in (b) using

d. Approximate f'(0.2) using P'4(0.2), and find the error.

04 f(x) dx usingP) dr. 0 Pa)dx.

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