Question

The value of \[ \lim_{x \to 0} \frac{x^3 \cot x}{1 - \cos x} \] is:

• A. 1
• B. 2
• C. -2
• D. 0

Hint:

When dealing with limits involving indeterminate forms, L'Hopital's Rule is a useful technique for simplifying and evaluating the limit.

Answer 1

The Correct Option is D

Step 1: The limit involves \( \cot x \) and \( 1 - \cos x \), both of which approach 0 as \( x \to 0 \). Use L'Hopital's Rule to evaluate the limit.
Step 2: After applying L'Hopital's Rule twice, the value of the limit is found to be 0.

Final Answer: \[ \boxed{0} \]