Question

Let F(x) = ∫ sin(t^2) dt from 0 to x Evaluate the limit

lim x--->0 (F(x)/x^2)

Answer 1

limit (x->0) (∫[0..x] sin(t^2) dt)/x^2 = 0

you can get some ideas if you study

https://www.wolframalpha.com/input/?i=limit+%28x-%3E0%29+%28%E2%88%AB%5B0..x%5D+sin%28t%5E2%29+dt%29%2Fx%5E2