The function is defined by

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The function

f

is defined by

f(x)=e^{kx}\cos x

, where

k

is a real constant. Its Maclaurin series is

f(x)=1+kx+\frac{k^{2}-1}{2}x^{2}+\frac{k^{3}-3k}{6}x^{3}+\cdots.

Measurements near

x=0

show that the series actually begins

1+5x+12x^{2}+\cdots

. Determine the value of

k