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Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives1 Mark
MCQ
$\lim_\limits{\text{x} \rightarrow 2}\Bigg(\frac{\sqrt{1-\text{cos}{2(\text{x}-2)}}}{\text{x}-2}\Bigg):$
  • ✓
    does not exist
  • B
    equals $ \sqrt{2}​$
  • C
    equals $-\sqrt{2}​$
  • D
    equals $\frac{-\sqrt{2}}{1}​$
✓

Answer

Correct option: A.
does not exist
$\lim_\limits{\text{t} \rightarrow 0}\frac{\sqrt{1-\cos2\text{t}}}{\text{t}}$
Clearly $\text{R.H.L}. = \sqrt{2}$​
$\text{L.H.L.} = -\sqrt{2}$
Since $\text{R.H.L}. \neq \text{L.H.L.}$
So, limit does not exist.
Hence, option $A$ is correct.

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