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1. This question is on the Taylor polynomial. (a) Find the Taylor Polynomial p3(x) for f(x)=...

1. This question is on the Taylor polynomial.

(a) Find the Taylor Polynomial p3(x) for f(x)= e^ x sin(x) about the point a = 0.

(b) Bound the error |f(x) − p3(x)| using the Taylor Remainder R3(x) on [−π/4, π/4].

(c) Let pn(x) be the Taylor Polynomial of degree n of f(x) = cos(x) about a = 0. How large should n be so that |f(x) − pn(x)| < 10^−5 for −π/4 ≤ x ≤ π/4 ?

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