pl help lim x-0 (integral from 0 to x cos(t^2) dt)/x

Question

anonymous · Answer

$$\lim_{x \rightarrow 0}[\int\limits_{0}^{x}\cos (t ^{2})dt]/x$$

anonymous · Answer

i think applying the l hospital rule will help but i cant differentiate the the upper part of the question that is$$d/dt[\int\limits_{0}^{x}\cos(t^2)dt]$$

agent47 · Answer

Isn't that just the fundamental theorem of calculus? Derivative and integral cancel each other out, so you end up with Cos(x^2)

anonymous · Answer

but then limit would become cos(x^2)/x=1/0=not defined the answer wont match

agent47 · Answer

http://www.wolframalpha.com/input/?i=Differentiate%28Integrate%28Cos%28t%5E2%29%2C+t%2C+0%2C+x%29%2C+x%29

anonymous · Answer

hey thanks i got it we have to differentiate both in numerator and denominator so on applying it would become cos(x^2)/1=1 thanks a lot

agent47 · Answer

yes

agent47 · Answer

I hadn't noticed that u didn't differentiate the denominator.

anonymous · Answer

yup same here i forgot to differentiate it