MCQ
$\mathop {\lim }\limits_{x \to 2} \frac{{\sqrt {1 + \sqrt {2 + x} } - \sqrt 3 }}{{x - 2}} = . . .$
- ✓$\frac{1}{{8\sqrt 3 }}$
- B$\frac{1}{{4\sqrt 3 }}$
- C$0$
- Dએકપણ નહી.
$ = \mathop {\lim }\limits_{x \to 2} \,\,\frac{{1 + \sqrt {2 + x} - 3}}{{(\sqrt {1 + \sqrt {2 + x} + \sqrt 3 )\,\,(x - 2)} }}$
$ = \mathop {\lim }\limits_{x \to 2} \,\,\frac{{\sqrt {2 + x} - 2}}{{(\sqrt {1 + \sqrt {2 + x} + \sqrt 3 )\,\,(x - 2)} }}$
$ = \mathop {\lim }\limits_{x \to 2} \,\,\frac{{(x - 2)}}{{(\sqrt {1 + \sqrt {2 + x} } + \sqrt 3 )\,\,(\sqrt {2 + x} + 2)\,\,(x - 2)}}$
$ = \frac{1}{{(2\sqrt 3 )\,4}} = \frac{1}{{8\sqrt 3 }}.$
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