Question

need help on that attachment @Calculus1

Answer 1

l'hopital is what you need

Answer 2

the limit is obviously 0 top and bottom so you have
\[\frac{0}{0}\]

Answer 3

so take the derivative in the numerator and denominator separately. you get
\[\frac{\sin(2\pi x^2)}{6x^2}\] remembering that the derivative of the integral is the integrand to find the derivative of that integral

Answer 4

now compute that limit, which you can do also with l'hopital if you like

Answer 5

not really necessary though because
\[\lim_{x\rightarrow 0}\frac{\sin(ax)}{bx}=\frac{a}{b}\]

Answer 6

so you will get
\[\frac{2\pi}{6}=\frac{\pi}{3}\]

Answer 7

Thanks!