Question

$\underset{x\to a}{lim}\frac{\sqrt{x-b}-\sqrt{a-b}}{x^2-a^2}$

Answer 1

${lim}_{x\to a}\frac{\sqrt{x-b}-\sqrt{a-b}}{x^2-a^2}=\frac{0}{0}$ form

Applying L-Hospital Rule

${lim}_{x\to a}\frac{\frac{1}{2\sqrt{x-b}}\left(1\right)}{2x}={lim}_{x\to a}\frac{1}{2x.2\sqrt{x-b}}$

$={lim}_{x\to a}\frac{1}{4x\sqrt{x-b}}=\frac{1}{4a\sqrt{a-b}}$