lim-x-0-0-x-2-4-t-3-dt-x-2-

Question Number 94723 by john santu last updated on 20/May/20

\lim_{x \to 0} \frac{\underset{0}{\int^{x^{2}}} \sqrt{4 + t^{3}} d t}{x^{2}} ?

Answered by i jagooll last updated on 20/May/20

Answered by mathmax by abdo last updated on 20/May/20

let use hospital rule we have \lim_{x \to 0} \frac{\int_{0}^{x^{2}} \sqrt{4 + t^{3}}}{x^{2}} dt

= \lim_{x \to 0} \frac{2 x \sqrt{4 + x^{6}}}{2 x} = \lim_{x \to 0} \sqrt{4 + x^{6}} = \sqrt{4} = 2