How do you use L'hospital's rule to find the limit ##lim_(x->oo)xsin(pi/x)## ?

The undetermination case is [infinity x 0], so we need to change it into one that we can use the L'Hospital rule with. This is the reason why we move ##x## at the denominator, as ##1/x##. This is the form that we can use the L'Hospital rule with. Be aware of the chain rule when differentiating ##sin (pi/x)##.