# Answer to Question #33276 in Calculus for nowhere1122

Question #33276

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

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

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