`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.

Asked on by enotes

Textbook Question

Chapter 4, 4.4 - Problem 41 - Calculus: Early Transcendentals (7th Edition, James Stewart).
See all solutions for this textbook.

1 Answer | Add Yours

gsarora17's profile pic

gsarora17 | (Level 2) Associate Educator

Posted on

`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`

We’ve answered 318,926 questions. We can answer yours, too.

Ask a question