Question

Solve :
$\underset{x\to 0}{lim}\frac{x}{3-\sqrt{x+9}}$

Answer 1

$\begin{array}{c}{lim}_{x\to 0}\frac{x}{3-\sqrt{x+9}}\\ ={lim}_{x\to 0}\frac{x}{\left(3-\sqrt{x+9}\right)}\frac{\left(3+\sqrt{x+9}\right)}{\left(3+\sqrt{x+9}\right)}\\ ={lim}_{x\to 0}\frac{x\left(3+\sqrt{x+9}\right)}{9-\left(x+9\right)}\\ ={lim}_{x\to 0}\frac{x\left(3+\sqrt{x+9}\right)}{-x}\\ ={lim}_{x\to 0}\frac{3+\sqrt{x+9}}{-1}\\ =-6\end{array}$