Question:
Find the value of the limit
\[
\lim_{x \to 0} \frac{\sqrt{1 - \cos x}}{x}
\]
Find the value of the limit
\[
\lim_{x \to 0} \frac{\sqrt{1 - \cos x}}{x}
\]
Show Hint
When encountering indeterminate forms like \( 0/0 \), apply L'Hopital's Rule to compute the limit.
Updated On: Jan 6, 2026
- 0
- 1
- \( \sqrt{2} \)
- does not exist
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Apply L'Hopital's Rule.
We have an indeterminate form \( 0/0 \), so we apply L'Hopital's Rule by differentiating the numerator and denominator.
Step 2: Conclusion.
After applying L'Hopital's Rule, the limit does not exist.
Final Answer: \[ \boxed{\text{does not exist}} \]
We have an indeterminate form \( 0/0 \), so we apply L'Hopital's Rule by differentiating the numerator and denominator.
Step 2: Conclusion.
After applying L'Hopital's Rule, the limit does not exist.
Final Answer: \[ \boxed{\text{does not exist}} \]
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