Question

Compute
\[\lim_{x\to 2}\frac{\int_{-2}^x \sin(t^3)\,dt}{x^4-16}\]

Answer 1

sin is odd, so as x goes to 2 the top and bottom are both going to 0. We can use L'hopitals rule and differentiate the numerator and denominator. On top we get sin(x^2). on the bottom we get 4x^3. Now we can plug in x=2.

the limit as x goes to 2 is sin(4)/(32).

Let me know if what I did is ok

Answer 2

Great! It is not very clear from above that what I wrote was sin(x^3)

Answer 3

oh allright then sin(8)/32