Question2.) (5pts) Evaluate the limit, if it exists. $$\lim _{x \rightarrow-2} \frac{x+2}{x^{3}+8}$$

Studdy Solution
Evaluate the limit of the simplified expression as $x \to -2$:
$$\lim_{x \to -2} \frac{1}{x^2-2x+4}$$
Substitute $x = -2$:
$$= \frac{1}{(-2)^2 - 2(-2) + 4}$$ $$= \frac{1}{4 + 4 + 4}$$ $$= \frac{1}{12}$$
The value of the limit is:
$$\boxed{\frac{1}{12}}$$