MCQ
$\mathop {\lim }\limits_{x \to a} \frac{{\sqrt {3x - a} - \sqrt {x + a} }}{{x - a}} = $
- A$\sqrt 2 a$
- ✓$1/\sqrt {2a} $
- C$2a$
- D$1/2a$
$ = \mathop {\lim }\limits_{x \to a} \,\frac{{\sqrt {3x - a} - \sqrt {x + a} }}{{(x - a)}} \times \frac{{\sqrt {3x - a} + \sqrt {x + a} }}{{\sqrt {3x - a} + \sqrt {x + a} }}$
$ = \frac{2}{{2\sqrt {2a} }} = \frac{1}{{\sqrt {2a} }}$
Aliter : Apply $L$- Hospital’s rule
$\mathop {\lim }\limits_{x \to a} \,\frac{{\sqrt {3x - a} - \sqrt {x + a} }}{{x - a}} = \mathop {\lim }\limits_{x \to a} \,\frac{3}{{2\,\sqrt {3x - a} }} - \frac{1}{{2\,\sqrt {x + a} }}$
$ = \frac{3}{{2\sqrt {2a} }} - \frac{1}{{2\sqrt {2a} }} = \frac{1}{{\sqrt {2a} }}.$
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