Question

L'HOPITAL rule Lim x-> Infinite x sin (10/x) Please explain

Answer 1

Ok:
Indeterminate of type 0*infinity
So we let t = 1/x
then now we have \[\lim_{x \rightarrow infinity} xsin(10/x) = \lim_{t \rightarrow 0} \sin(10t)/(t) \] which is:
\[\lim_{t \rightarrow 0} 10\cos(10t) \] from applying L'Hopital.
Now plug in t and see that the limit goes to 10.

Answer 2

Make sense?

Answer 3

yes it does. thank you!