The value of limx→2a x−2a+x−2ax2−4a2, is

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

Solution:

We have,

$\begin{array}{l} lim_{x \to 2 a} \frac{\sqrt{x - 2 a} + \sqrt{x} - \sqrt{2 a}}{\sqrt{x^{2} - 4 a^{2}}} \\ = lim_{x \to 2 a} \frac{\sqrt{x - 2 a} + \frac{x - 2 a}{\sqrt{x} + \sqrt{2 a}}}{\sqrt{(x - 2 a)} \sqrt{(x + 2 a)}} \\ = lim_{x \to 2 a} \frac{1 + \frac{\sqrt{x - 2 a}}{(\sqrt{x} + \sqrt{2 a})}}{(\sqrt{x + 2 a)}} = \frac{1}{\sqrt{4 a}} = \frac{1}{2 \sqrt{a}} \end{array}$

The value of $lim_{x \to 2 a} \frac{\sqrt{x - 2 a} + \sqrt{x} - \sqrt{2 a}}{\sqrt{x^{2} - 4 a^{2}}}$ , is

Solution:

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