Question

Apply the limits $\underset{x\to 3}{Lt}\frac{x-3}{\sqrt{|x^2-9|}}$

Answer 1

$\underset{x\to 3}{lim}\frac{x-3}{\sqrt{\left(x^2-9\right)}}$ $\left(÷form\right)$

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

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

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

$=0$