Answer to Question #33276 in Calculus for nowhere1122

Question

Let f(x ) = e^x cos(x ) . The power series expansion of f(x) centered at 0 is f(x) = 1 + x - x^3 /3 - x^4 /6 + c5 x^5 + x^7 / 630 + ...
a) show that c5 = - 1/30
b) estimate integral from 0 to 1 e^x cos(x) dx using the given series.
c) estimate f'(1) using the given series