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

Find the limits
$\underset{x\to -3}{lim}\frac{2-\sqrt{{x}^{2}-5}}{x+3}$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Arham Warner
Given Data
The limit is $\underset{x\to -3}{lim}\frac{2-\sqrt{{x}^{2}-5}}{x+3}$
Solve the given limit expression,
$L=\underset{x\to -3}{lim}\frac{2-\sqrt{{x}^{2}-5}}{x+3}$
$=\frac{2-\sqrt{\left(-3{\right)}^{2}-5}}{-3+3}$
$=\frac{2-\sqrt{9-5}}{0}$
$=\mathrm{\infty }$
The value of limit is $\mathrm{\infty }$ so it means that the sequence diverge.
Hence the limit does not exists and sequence diverge.