Question

Find the limits lim_{xrightarrow-3}frac{2-sqrt{x^2-5}}{x+3}

Limits and continuity
Find the limits
$$\lim_{x\rightarrow-3}\frac{2-\sqrt{x^2-5}}{x+3}$$

2020-10-24
Given Data
The limit is $$\lim_{x\rightarrow-3}\frac{2-\sqrt{x^2-5}}{x+3}$$
Solve the given limit expression,
$$L=\lim_{x\rightarrow-3}\frac{2-\sqrt{x^2-5}}{x+3}$$
$$=\frac{2-\sqrt{(-3)^2-5}}{-3+3}$$
$$=\frac{2-\sqrt{9-5}}{0}$$
$$=\infty$$
The value of limit is $$\infty$$ so it means that the sequence diverge.
Hence the limit does not exists and sequence diverge.