Question

Evaluate the limit:

\[ \lim_{x \to 0} \frac{x^2}{\sin x} \]

= _______.

• A. 0
• B. 1
• C. 2
• D. -1

Hint:

When evaluating limits involving \( \sin x \), use the approximation \( \sin x \approx x \) as \( x \to 0 \).

Answer 1

The Correct Option is A

We are tasked with evaluating the limit: \[ \lim_{x \to 0} \frac{x^2}{\sin x}. \] Step 1: Analyze the limit. 
As \( x \to 0 \), \( \sin x \approx x \). Thus, we can approximate the limit as: \[ \lim_{x \to 0} \frac{x^2}{\sin x} \approx \lim_{x \to 0} \frac{x^2}{x} = \lim_{x \to 0} x = 0. \] Therefore, the value of the limit is 0. 
Final Answer: \[ \boxed{\text{(A) 0}}. \]