Question

Calculate the following limits.
$\underset{x\to -3}{lim}\frac{x+3}{\sqrt{x+4}-1}.$

Answer 1

$\underset{x\to -3}{lim}\frac{x+3}{\sqrt{x+4}-1}$

$=\underset{x\to -3}{lim}\frac{x+3}{\sqrt{x+4}-1}\frac{\sqrt{x+4}+1}{\sqrt{x+4}+1}$

$=\underset{x\to -3}{lim}\frac{(x+3)(\sqrt{x+4}+1)}{x+4-1}$

$=\underset{x\to -3}{lim}\frac{(x+3)(\sqrt{x+4}+1)}{x+3}$

$=\underset{x\to -3}{lim}(\sqrt{x+4}+1)$

$=2$