JEE Mains · Maths · STD 11 - 12. limits
The value of \(\lim\limits _{x \rightarrow 1} \frac{\left(x^{2}-1\right) \sin ^{2}(\pi x)}{x^{4}-2 x^{3}+2 x-1}\) is equal to
- A \(\frac{\pi^{2}}{6}\)
- B \(\frac{\pi^{2}}{3}\)
- C \(\frac{\pi^{2}}{2}\)
- D \(\pi^{2}\)
Answer & Solution
Correct Answer
(D) \(\pi^{2}\)
Step-by-step Solution
Detailed explanation
\(\lim \limits_{x \rightarrow 1} \frac{\left(x^{2}-1\right) \sin ^{2} \pi x}{\left(x^{2}-1\right)(x-1)^{2}}=\lim \limits_{x \rightarrow 1}\left(\frac{\sin ((1-x) \pi))}{\pi(1-x)}\right)^{2} \pi^{2}=\pi^{2}\)
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