Evaluate the limit:
\[
\lim_{x \to 0} \frac{x^2}{\sin x}
\]
= _______.
\[ \lim_{x \to 0} \frac{x^2}{\sin x} \]
= _______.Show Hint
- 0
- 1
- 2
- -1
The Correct Option is A
Solution and Explanation
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: \[ \boxed{\text{(A) 0}}. \]
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