Question

Find the value of the limit \[ \lim_{x \to 0} \frac{\sqrt{1 - \cos x}}{x} \]

• A. 0
• B. 1
• C. \( \sqrt{2} \)
• D. does not exist

Hint:

When encountering indeterminate forms like \( 0/0 \), apply L'Hopital's Rule to compute the limit.

Answer 1

The Correct Option is D

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: \[ \boxed{\text{does not exist}} \]