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

question 76

Multiple Choice

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

• A) 31
• B) 28
• C) 35
• D) 25