AP Calculus AB help dealing with limits!?

Question

We just learned the sandwich theorem and I am really confused on it.

The problem is limit(as x-->0)[x*sin(1/x)]

We have to use the sandwich theorem to solve it.

Thank you SO much, in advance!

Answer 1

The trick here is to realize that no matter what the value of x, sin(1/x) will always remain between -1 and 1.  

So, using the sandwich theroem, the limit of the problem is between

x*1 and x*(-1).

as x-->0, x*1 -->0 and x*(-1) --> 0.  

Thus, the limit is 0.  

Good luck!