Limits and Continuity

Evaluate $\lim_{x \to 2} \frac{\sqrt{x+2} - 2}{x^3 - 8}$.

Evaluate $\lim_{x \to 2} \frac{\sqrt[3]{x+6} - 2}{x-2}$.

A car's speed (in m/s) is given by $v(t) = \frac{t^3 - 27}{t^2 - 9}$ for $t \neq 3$. Find $\lim_{t \to 3} v(t)$, the limiting speed as time approaches 3 seconds.