1. The problem statement, all variables and given/known data The Fresnel function is given as S(x) = ∫sin(3πt^2)dt from 0 to x. Find the limit as x approaches 0 of S(x)/4x^3 2. Relevant equations 3. The attempt at a solution I took the derivative of the S(x) function to be able to plug x in. I then used L'Hospital's rule after getting 0/0. I took the derivative a second time after getting 0/0 again. My final answer was π/2, which is wrong. The other answer choices are π/4, 3π/2, 1/2, and 1/4. sin(3πx^2)/4x^3 ; took derivative of top and bottom and got (6πx)(cos(3πx^2)/12x. Plugged in 0 and got 0/0. Took derivative of top and bottom again and got, (cos3πx^2)(6π)+(6πx)(-sin(3πx^2)(6πx). Plugged in 0 and got π/2 as final answer. Where did I go wrong and what is the right answer?