Answer
$x=-1$
Work Step by Step
We are given the function:
$h(x)=\dfrac{e^x}{(x+1)^3}$
Compute $\lim\limits_{x \to a} h(x)=\lim\limits_{x \to a} \dfrac{e^x}{(x+1)^3}$
The denominator is 0 for $x=-1$. For $a=-1$ we have:
$\lim\limits_{x \to -1^-} \dfrac{e^x}{(x+1)^3}=-\infty$
$\lim\limits_{x \to -1^+} \dfrac{e^x}{(x+1)^3}=\infty$
Therefore $h(x)$ has a vertical asymptote in $x=-1$.
