# Thread: A trigonometric limit problem

1. ## A trigonometric limit problem

I took a quiz today, and I messed up on this question.

Limit of (sin x^1/3)/(x^1/3)

I put down 1 as the answer, but I didn't know how to show my work. All I did was memorize the special limit. Is there another way to do this besides the sandwich theorem?

Thank you

2. Originally Posted by Wyau
I took a quiz today, and I messed up on this question.

Limit of (sin x^1/3)/(x^1/3)

I put down 1 as the answer, but I didn't know how to show my work. All I did was memorize the special limit. Is there another way to do this besides the sandwich theorem?

Thank you
i suppose it was the limit as x goes to zero?

you could use L'Hopital's rule if you learned it

3. $\lim_{u\to0}\frac{\sin u}u=1$

What about if you define a change of variables according to $u=x^{1/3}$?