Let $f$ be a differentiable function with $f(3) \neq 0$. Evaluate $\displaystyle\lim_{x \to \infty} \left(\frac{f(3 + 1/x)}{f(3)}\right)^x$. (A) $e^{f'(3)/f(3)}$ (B) $e^{f(3)}$ (C) $e^{f'(3)}$ (D) 1
(A) $e^{f'(3)/f(3)}$
Let $f$ be a differentiable function with $f(3) \neq 0$. Evaluate $\displaystyle\lim_{x \to \infty} \left(\frac{f(3 + 1/x)}{f(3)}\right)^x$.
(A) $e^{f'(3)/f(3)}$ \quad (B) $e^{f(3)}$ \quad (C) $e^{f'(3)}$ \quad (D) 1