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

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

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.