#### Answer

\[ = \frac{3}{4}\]

#### Work Step by Step

\[\begin{gathered}
\mathop {\lim }\limits_{x \to 0} \,\,\frac{{3{{\sec }^5}x}}{{{x^2} + 4}} \hfill \\
\hfill \\
let\,\,x = 0\,\, \hfill \\
\hfill \\
then \hfill \\
\hfill \\
= \frac{{3\,{{\sec }^5}\,\left( 0 \right)}}{{\,{{\left( 0 \right)}^2} + 4}} \hfill \\
\hfill \\
simplify \hfill \\
\hfill \\
= \frac{{3\,\left( 1 \right)}}{{0 + 4}} \hfill \\
\hfill \\
= \frac{3}{4} \hfill \\
\hfill \\
\end{gathered} \]