Question

Evaluate $\underset{x\to 1}{lim}\frac{\sqrt{3+x}-\sqrt{5-x}}{x^2-1}$

Answer 1

Limit is of form $\frac{0}{0}$, applying l'opital,

$L=\underset{x\to 1}{lim}\frac{\frac{1}{2\sqrt{3+x}}+\frac{1}{2\sqrt{5-x}}}{2x}=(\frac{1}{2\left(2\right)}+\frac{1}{2\left(2\right)})\frac{1}{2}$

$=\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}$.