JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

The value of

\lim \limits_{{x \rightarrow \pi / 2}}\left\{1^{\sec ^2 x}+2^{\sec ^2 x}+3^{\sec ^2 x}+\ldots .+n^{\sec ^2 x}\right\}^{\cos ^2 x},

View answer and explanation

Correct option: B

n

Option B (

n

) is correct because, as

x

approaches

\pi/2

, the expression simplifies to

n

after applying limit properties and L'Hôpital's rule implicitly.

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\lim \limits_{{x \rightarrow 0}}\left(\frac{1}{x^2}-\operatorname{cosec}^2 x\right)

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\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\}

\lim \limits_{{x \rightarrow \infty}} x\left(e^{1 / x}-1\right)

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