AP

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

f(x)=\ln x

and

g(x)=\sqrt{x}

. (i) State the formal definition of the limit of a function as

x\to \infty

. (ii) Evaluate

\displaystyle \lim_{x\to \infty}\frac{\ln x}{\sqrt{x}}

. Show all steps clearly. (iii) Using your answer to part (ii), explain which of the two functions

f(x)

g(x)

grows faster for very large positive values of

x

. Justify your conclusion in one or two sentences.