Provide an Appropriate Response $\lim _ { \mathrm { n } \rightarrow\infty } \frac { \ln \mathrm { n } } { \mathrm { n } ^ { \mathrm { c } } } = 0$

Multiple Choice

Provide an appropriate response.
-It can be shown that $\lim _ { \mathrm { n } \rightarrow\infty } \frac { \ln \mathrm { n } } { \mathrm { n } ^ { \mathrm { c } } } = 0$ for $\mathrm { c } > 0$ . Find the smallest value of $\mathrm { N }$ such that $\left| \frac { \ln \mathrm { n } } { \mathrm { n } ^ { \mathrm { c } } } \right| < \varepsilon$ for all $\mathrm { n } > \mathrm { N }$ if $\varepsilon = 0.01$ and $c = 1.8$ .

A) 35
B) 25
C) 28
D) 31