Answer
$\lim\limits_{x \to -3} \frac{1}{(x+3)^4} = \infty$
Work Step by Step
Let $M \gt 0$ be given.
Let $\delta = (\frac{1}{M})^{1/4}$
Suppose that $\vert x-(-3) \vert \lt \delta$
Then:
$\vert \frac{1}{(x+3)^4}\vert \gt \vert \frac{1}{\delta^4} \vert = \vert \frac{1}{1/M} \vert = M$
Therefore, $\lim\limits_{x \to -3} \frac{1}{(x+3)^4} = \infty$
