Answer
We can guess here that $$\lim_{x\to3}\frac{x^2-9}{\sqrt{x^2+7}-4}=8$$
Work Step by Step
$$\lim_{x\to3}\frac{x^2-9}{\sqrt{x^2+7}-4}$$
(a) The graph is shown below.
(b) Looking at the graph, as $x\to3$, we see that $\frac{x^2-9}{\sqrt{x^2+7}-4}$ approaches as close as $8$.
Therefore, we can guess here that $$\lim_{x\to3}\frac{x^2-9}{\sqrt{x^2+7}-4}=8$$
