Answer
$\ln 3$
Work Step by Step
Let $\lim\limits_{\theta \to 0}f(x)=\lim\limits_{\theta \to 0} \dfrac{3^{ \sin\theta}-1}{\theta}$
But $f(0)=\dfrac{0}{0}$
This shows that the limit has an indeterminate form, so we need to apply L-Hospital's rule as follows: $\lim\limits_{m \to n}f(x)=\lim\limits_{m \to n}\dfrac{p'(x)}{q'(x)}$
This implies that
$\lim\limits_{\theta \to 0}\dfrac{(3^{ \sin\theta})(\ln 3) (\cos \theta)}{1}=(3^{ \sin (0)})(\ln 3) (\cos (0))$
Thus, $(1) (\ln 3) (1)=\ln 3$
