TS EAMCET · Maths · Limits
\(\lim _{x \rightarrow 0} x^2 \sin \frac{\pi}{x}\) is equal to
- A 1
- B 0
- C does not exist
- D \(\infty\)
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \lim _{x \rightarrow 0} x^2 \sin \left(\frac{\pi}{x}\right) \\ &=\lim _{x \rightarrow 0} \pi x \cdot \frac{\sin \frac{\pi}{x}}{\frac{\pi}{x}}=0(1)=0\end{aligned}\)
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