Question

evaluate

Answer 1

\[\lim_{x \rightarrow 0} \frac{ S(x) }{ x ^{3} } where S(x) = \int\limits_{0}^{x} \sin (\frac{ 1 }{ 2} \Pi t ^{2})dt\]

Answer 2

you mean sin (pi t^2/2)?

Answer 3

yes

Answer 4

let me try. take a while

Answer 5

do you know fundamental theorem of calculus and L'hopital's rule?