Let , where is a non-negative real constant. For which value of does…

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

Problem

Let

f_k(x)=\dfrac{6x^{4}+x^{2}}{k e^{x}+3x^{4}}

, where

k

is a non-negative real constant. For which value of

k

does

\displaystyle\lim_{x\to\infty} f_k(x)=2

? (a)

k=3

(b) Every

k\ge 0

(c)

0

(d) No such

k