`lim_(x->oo) xsin(pi/x)` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply,...

`lim_(x->oo) xsin(pi/x)` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why.

Expert Answers
gsarora17 eNotes educator| Certified Educator

`lim_(x->oo)xsin(pi/x)`

`=lim_(x->oo)sin(pi/x)/(1/x)`

Apply L'Hospital rule , Test condition:0/0

`=lim_(x->oo)(sin(pi/x)')/((1/x)')`

`=lim_(x->oo)(cos(pi/x)(-pix^-2))/(-1x^-2)`

`=lim_(x->oo)picos(pi/x)`

plug in the value,

`=picos(pi/oo)`

`=picos(0)`

`=pi`