Question

Solve
${lim}_{x\to a}\frac{\sqrt{x-b}-\sqrt{a-b}}{x^2-a^2}(a>b)$

Answer 1

Solve ${lim}_{x\to a}\frac{\sqrt{x-b}-\sqrt{a-b}}{x^2-a^2}$ $(a>b).$

${lim}_{x\to a}\frac{\sqrt{x-b}-\sqrt{a-b}}{x^2-a^2}$ $\left(\frac{0}{0}form\right)$

${lim}_{x\to a}\frac{\frac{1}{2}(x-b)\frac{-1}{2}}{2x}$

$=\frac{1}{2}\frac{(a-b)\frac{-1}{2}}{2a}$

$=\frac{1}{4a(a-b{)}^{1/2}}$

$=\frac{1}{4a\sqrt{a-b}}$