Limits & Continuity: lim_xto0(48)/(x^4)int_0^x(t^3)/(t^6+1)dt is equal to ______. | JEE Main 2023 | Yukti Vault

Yukti Vault

JEE Main 2023 (Online) 30th January Morning ShiftQuestion 1

$\lim_{x\to0}\frac{48}{x^4}\int_0^x\frac{t^3}{t^6+1}dt$ is equal to ______.

Limits & Continuity

Answer$12$

Solution

By L'Hospital, the limit is $\lim\frac{48}{4x^3}\cdot\frac{x^3}{x^6+1}=12$.

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