$\mathop {\lim }\limits_{x \to 0} \,\,\frac{{\mathop \smallint \nolimits_0^{{x^2}} \,\,\sin \,\,\sqrt t \,\,dt}}{{{x^3}}}$ is equal to

JEE MATHEMATICS MCQ: LIMITS

1 Easy

1 of 1

Application +4 | -1

\lim\limits_{x \to 0} \,\,\frac{{\int \nolimits_0^{{x^2}} \,\,\sin \,\,\sqrt t \,\,dt}}{{{x^3}}}

is equal to

View answer and explanation

Correct option: C

2/3

Option C (

2/3

) is correct because applying L'Hospital's rule yields the limit as

2/3

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