Maths · Limits, continuity and differentiability
Assertion does not exist. Reason
Assertion \( \lim _{\boldsymbol{x} \rightarrow \mathbf{0}} \frac{\sqrt{1-\cos 2 x}}{\boldsymbol{x}} \) does not exist. Reason \( |\sin x|=\left\{\begin{array}{cc}\sin x ; & 0<x<\frac{\pi}{2} \\ -\sin x ; & -\frac{\pi}{2}<x<0\end{array}\right. \)
- A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
- B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
- C. Assertion is correct but Reason is incorrect
- D. Assertion is incorrect but Reason is correct
Step-by-step solution
The limit simplifies to √2 * |sin x|/x. Using the definition of |sin x|, the right-hand limit is √2 and left-hand limit is -√2, so the limit does not exist. The reason correctly states the piecewise definition of |sin x|, which is used to evaluate the limit.
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