Question

Evaluate :$\underset{x\to 0}{lim}\frac{x^2+\sqrt{x+6}-12}{x^2-9}$

Answer 1

${lim}_{x\to 0}\frac{x^2+\sqrt{x+6}-12}{x^2-9}$

$=\frac{0+\sqrt{0+6}-12}{0-9}$

$=\frac{\sqrt{6}-12}{-9}$

$=\frac{12-\sqrt{6}}{9}$