For a real parameter

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

a

, define

f_a(x)=x^{a}

and let

g(x)=\ln x

for

x>1

. Determine all real values of

a

for which

f_a

grows faster than

g

x\to\infty

, and justify your answer using an appropriate limit.