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  4. The value of displaystyle lim x arrow 1 ((x2-1) sin 2(π x)/x4-2 x3+2 x-1) is equal to:

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Q. The value of $\displaystyle\lim _{x \rightarrow 1} \frac{\left(x^{2}-1\right) \sin ^{2}(\pi x)}{x^{4}-2 x^{3}+2 x-1}$ is equal to:

JEE MainJEE Main 2022Limits and Derivatives

Solution:

$\displaystyle\lim _{x \rightarrow 1} \frac{\left(x^{2}-1\right) \sin ^{2} \pi x}{\left(x^{2}-1\right)(x-1)^{2}}=\displaystyle\lim _{x \rightarrow 1}\left(\frac{\sin ((1-x) \pi))}{\pi(1-x)}\right)^{2} \pi^{2}=\pi^{2}$