_ x 2 ( 1-cos 2(x-2) x-2 ): - Vidyadip

MCQ

$\lim_\limits{\text{x} \rightarrow 2}\Bigg(\frac{\sqrt{1-\text{cos}{2(\text{x}-2)}}}{\text{x}-2}\Bigg):$

A
does not exist
B
equals $ \sqrt{2}$
C
equals $-\sqrt{2}$
D
equals $\frac{-\sqrt{2}}{1}$

✓

Answer

does not exist

Solution:

$ \lim_\limits{\text{t} \rightarrow 0}\frac{\sqrt{1-\cos2\text{t}}}{\text{t}}$

Clearly R.H.L. = $ \sqrt{2}$

L.H.L. = $ -\sqrt{2}$

Since R.H.L.$ \neq$ L.H.L. So, limit does not exist.

Hence, option A is correct.

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