The Limit of xsin(1/x) as x Goes to Infinity

In this short video I show how to find the limit of xsin(1/x) as x goes to infinity. I show how to make a substitution into the limit, then use the idea that the limit as x goes to 0 of sinx/x = 1.

This limit can also be evaluated using L'Hopital's Rule, but I am assuming that the viewer has not learned derivatives yet.

This topic appears in the limits and continuity unit of Calculus 1 and AP Calculus AB/BC.