Need help with Calculus Problem: L'Hopital's Rule?

Question

I need assistance with a problem regarding L'Hopital's Rule. I'm not trying to cheat on my homework, I just need to know how to do this problem, so I'd prefer an explanation along with an answer.

The problem is as follows:

lim (as x approaches infinity) of xsin(37/x)

Using L'Hopital's Rule, how do I find the limit of this particular problem? I think I've put it in an indeterminate form, but it's not converging >_<

Thanks!

Answer 1

x sin(37/x) = sin(37/x) / (1/x)---&gt; 37 [sin (37/x) / (37/x)]----&gt; 37 without L&#039;Hopital&#039;s  rule....you could use t = 37 / x, t ---&gt;0 as x---&gt; ∞