MCQ
$\mathop {{\rm{lim}}}\limits_{x \to 2} \left( {\frac{{\sqrt {1 - {\rm{cos}}\left\{ {2\left( {x - 2} \right)} \right\}} }}{{x - 2}}} \right)$
- A$\sqrt 2 $
- B-$\;\sqrt 2 $
- C$\frac{1}{{\sqrt 2 }}$
- ✓અસ્તિત્વ નથી.
$ = \mathop {\lim }\limits_{x \to 2} \frac{{\sqrt 2 |\sin (x - 2)|}}{{x - 2}}$
$R.H.L. = \mathop {\lim }\limits_{x \to {2^ - }} \frac{{\sqrt 2 \sin (x - 2)}}{{(x - 2)}} = - \sqrt 2 $
$R.H.L. = \mathop {\lim }\limits_{x \to {2^ + }} \frac{{\sqrt 2 \sin (x - 2)}}{{(x - 2)}} = - \sqrt 2 $
Thus $L . H . L . \neq R . H . L$
Hence, $\mathop {\lim }\limits_{x \to 2} \frac{{\sqrt {1 - \cos \{ 2(x - 2)\} } }}{{x - 2}}$ does not exist.
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