The value of limx→a x−b−a−bx2−a2(a>b) is

A
$\frac{1}{4 a}$
B
$\frac{1}{a \sqrt{a - b}}$
C
$\frac{1}{2 a \sqrt{a - b}}$
D
$\frac{1}{4 a \sqrt{a - b}}$

Solution:

$\begin{array}{l} \frac{\sqrt{x - b} - \sqrt{a - b}}{x^{2} - a^{2}} \\ = \frac{(x - b) - (a - b)}{(x - a) (x + a)} \frac{1}{\sqrt{x - b} + \sqrt{a - b}} \\ = \frac{1}{(x + a) (\sqrt{x - b} + \sqrt{x - a})} \end{array}$

Required limit = $\frac{1}{2 a \cdot 2 \sqrt{a - b}} = \frac{1}{4 a \sqrt{a - b}}$ .

The value of $lim_{x \to a} \frac{\sqrt{x - b} - \sqrt{a - b}}{x^{2} - a^{2}} (a > b)$ is

Solution:

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