The value of $\mathop {\lim }\limits_{x - 0} \frac{1}{{{x^3}}}\mathop \smallint \nolimits_0^x \frac{{t\log \left( {1 + t} \right)}}{{{t^4} + 4}}dt$ is

JEE MATHEMATICS MCQ: LIMITS

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The value of

\lim\limits_{x - 0} \frac{1}{{{x^3}}}\int \nolimits_0^x \frac{{t\log \left( {1 + t} \right)}}{{{t^4} + 4}}dt

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Correct option: B

\frac{1}{{12}}

Option B (

\frac{1}{{12}}

) is correct because using L'Hopital's rule, the limit simplifies to

\frac{1}{{12}}

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