Consider . Which statement about the horizontal asymptote(s) of is…

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

Problem

Consider

k(x)=\dfrac{x^{2}}{e^{x}}+\dfrac{\cos x}{x}

. Which statement about the horizontal asymptote(s) of

k

is correct? (a)

k

has no horizontal asymptotes because the term

\dfrac{x^{2}}{e^{x}}

grows without bound. (b)

k

has a horizontal asymptote

y=0

for both

x\to +\infty

and

x\to -\infty

. (c)

k

has a single horizontal asymptote

y=0

x\to +\infty

, but none as

x\to -\infty

. (d)

k

has no horizontal asymptotes because the term

\dfrac{\cos x}{x}

continues to oscillate.