What is the limit of this specific function? Please evaluate the following limit for me:
$$\lim_{x \to -1} \frac{\sqrt{x^2+8}-3}{x+1} $$
I'd tried my best to solve this but unfortunately, it's too difficult for me. I tried multiplying by its conjugate and factoring the $x^2$ out but I can't get rid of that $x+1$ in the denominator so it always stay in the indeterminate form.

Use L'hopital's rule (Valid since the function is of the form $\frac{0}{0}$). The derivative of the top has limt equal to $-\frac{1}{3}$ and the derivative of the denominator is the constant $1$.
