Mathematics

Problem

Rank the following functions from slowest to fastest growth as

x\to\infty

: I.

\ln x

II.

x^{1/2}

III.

e^{\sqrt{x}}

\text{III}<\text{II}<\text{I}

\text{I}<\text{II}<\text{III}

\text{II}<\text{I}<\text{III}

\text{I}<\text{III}<\text{II}