Mathematics

Problem

Define

p(x)=e^{x}\cos x

. (a) Write the first five non-zero terms of the Maclaurin series for

e^{x}

. (b) Write the first five non-zero terms of the Maclaurin series for

\cos x

. (c) Using parts (a) and (b), compute the first five non-zero terms of the Maclaurin series for

p(x)

. Present the result in ascending powers of

x

. (d) Determine the radius of convergence of the Maclaurin series obtained in part (c) and justify your conclusion.