The value of $\mathop {\lim }\limits_{x \to 0} \,\,\frac{{\int_t^x {t{\rm{ }}dt} \,\,}}{{x\tan \left( {x + \pi } \right)}}$ is equal to

JEE MATHEMATICS MCQ: LIMITS

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The value of

\lim\limits_{x \to 0} \,\,\frac{{\int_t^x {t\mathrm{ }dt} \,\,}}{{x\tan \left( {x + \pi } \right)}}

is equal to

View answer and explanation

Correct option: C

\frac{1}{2}

Option C (

\frac{1}{2}

) is correct because, by applying L'Hopital's rule or direct integration and simplification, the limit evaluates to 1/2.

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