The value of $\mathop {\lim }\limits_{x \to 0} \left( {\frac{{\mathop \smallint \nolimits_0^{{x^2}} {{\sec }^2}t{\rm{ }}dt}}{{x\sin x}}} \right)$ is

JEE MATHEMATICS MCQ: LIMITS

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The value of

\lim\limits_{x \to 0} \left( {\frac{{\int \nolimits_0^{{x^2}} {{\sec }^2}t\mathrm{ }dt}}{{x\sin x}}} \right)

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Correct option: C

Option C (1) is correct because after applying L'Hopital's rule, the limit evaluates to 1.

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