For positive integers

MATHEMATICS · Single correct · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

k

, the limit

\displaystyle \lim_{x \to \infty} \frac{x^{k}}{\ln x}

is considered. Select the smallest integer value of

k

for which this limit is infinite. (a)

k=2

(b)

k=1

(c)

k=0

(d)

k=3