QuestionEvaluate $\lim _{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x^{2}-49}$

Studdy Solution
Re-evaluate the limit as $x$ approaches 7:
$\lim _{x \rightarrow 7} \frac{1}{(x+7)(\sqrt{x+2}+3)} = \frac{1}{(7+7)(\sqrt{7+2}+3)}$
Simplify:
$= \frac{1}{14 \times (3+3)} = \frac{1}{14 \times 6} = \frac{1}{84}$
The value of the limit is:
$\boxed{\frac{1}{84}}$