AP EAMCET · Maths · Limits
The limit \(\lim _{x \rightarrow 1} \frac{\sqrt{1-\cos 2(x-1)}}{x-1}\)
- A exists and is equal to \(\sqrt{2}\)
- B exists and is equal to \(-\sqrt{2}\)
- C does not exist
- D exists and is equal to \(\left(\frac{1}{2}\right)\)
Answer & Solution
Correct Answer
(C) does not exist
Step-by-step Solution
Detailed explanation
\text { Let } \begin{array}{rlr} L & =\lim _{x \rightarrow 1} \frac{\sqrt{1-\cos 2(x-1)}}{x-1} & \\ & =\lim _{x \rightarrow 1} \frac{\sqrt{2 \sin ^2(x-1)}}{x-1} \quad\left[\because 1-\cos 2 \theta=2 \sin ^2 \theta\right] \\ & =\sqrt{2} \lim _{x \rightarrow 1} \frac{|\sin…
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