Mathematics

Problem

Which one of the following best describes the behaviour of the function

f(x)=e^{-3x}\cos x

x\to\infty

? a)

f(x)

oscillates between

-1

and

1

without tending to any number. b)

f(x)

grows without bound. c)

f(x)

approaches

0

. d)

f(x)

oscillates with decreasing amplitude and hence has no limit.