MCQ
$\lim_\limits{\text{x} \rightarrow 2}\Bigg(\frac{\sqrt{1-\text{cos}{2(\text{x}-2)}}}{\text{x}-2}\Bigg):$
- Adoes not exist
- Bequals $ \sqrt{2}$
- Cequals $-\sqrt{2}$
- Dequals $\frac{-\sqrt{2}}{1}$
✓
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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