$\mathop {\lim }\limits_{x \to \infty } \frac{{\mathop \smallint \nolimits_0^{2x} x{e^{{x^2}}}dx}}{{{e^{4{x^2}}}}}$ equals

JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

\lim\limits_{x \to \infty } \frac{{\int \nolimits_0^{2x} x{e^{{x^2}}}dx}}{{{e^{4{x^2}}}}}

equals

View answer and explanation

Correct option: D

\frac{1}{2}

Option D (

\frac{1}{2}

) is correct because evaluating the integral and applying L'Hopital's rule results in the answer

\frac{1}{2}

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