The value of $\mathop {\lim }\limits_{x \to 1} \left( {1 - x} \right)\tan \left( {\frac{{\pi x}}{2}} \right)$, is

JEE MATHEMATICS MCQ: LIMITS

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The value of

\lim\limits_{x \to 1} \left( {1 - x} \right)\tan \left( {\frac{{\pi x}}{2}} \right)

, is

View answer and explanation

Correct option: C

\frac{2}{\pi }

Option C (

\frac{2}{\pi }

) is correct because the limit is evaluated using L'Hopital's rule or by rewriting the expression using trigonometric identities and then applying standard limits.

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The value of

\lim\limits_{h \to 0} 2\left\{ {\frac{{\sqrt 3 \sin \left( {\frac{\pi }{6} + h} \right) - \cos \left( {\frac{\pi }{6} + h} \right)}}{{\sqrt 3 h\left( {\sqrt 3 \cos \,h - \sin \,h} \right)}}} \right\}

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, then the value of

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is equal to

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equals