For real numbers

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

Problem

For real numbers

k

, let

L(k)=\lim_{x\to\infty}\frac{x^{k}}{e^{x}}.

Which of the following correctly describes

L(k)

? (a)

L(k)=0

only when

k>0

. (b)

L(k)=\infty

when

k>1

and

0

otherwise. (c)

L(k)=0

for every real

k

. (d)

L(k)

does not exist for any real

k

because the expression oscillates.