Question

Evaluate:-

$\underset{x\to 36}{lim}\frac{x-36}{\sqrt{x}-6}$

Answer 1

${lim}_{x\to 36}\frac{x-36}{\sqrt{x}-6}$

$={lim}_{x\to 36}\frac{x-36}{\sqrt{x}-6}\times \frac{\sqrt{x}+6}{\sqrt{x}+6}$

$={lim}_{x\to 36}\frac{(x-36)(\sqrt{x}+6)}{x-36}$

$={lim}_{x\to 36}\sqrt{x}+6=\sqrt{36}+6=6+6=12$