Answer
$\dfrac{1}{2}$
Work Step by Step
Here, we have $\lim\limits_{h \to 0} f(0)=\dfrac{0}{0}$
This shows an indeterminate form of limit, thus we will apply L-Hospital's rule such as:
$\lim\limits_{x \to \infty} f(x)=\lim\limits_{x \to \infty} \dfrac{p'(x)}{q'(x)}$
$\lim\limits_{h \to 0} \dfrac{e^h-1}{2h}=\dfrac{0}{0}$
Now, again apply L-Hospital's rule.
$\lim\limits_{h \to 0} \dfrac{e^h}{2}=\dfrac{e^{0}}{2}=\dfrac{1}{2}$
