Homework Help

Determine limit `lim_(x->oo) ((cos (1/x))^x)^2`

user profile pic

xalal | (Level 1) Honors

Posted June 25, 2013 at 5:47 PM via web

dislike 0 like

Determine limit `lim_(x->oo) ((cos (1/x))^x)^2`

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 25, 2013 at 5:59 PM (Answer #1)

dislike 1 like

The limit `lim_(x->oo) ((cos (1/x))^x)^2` has to be determined.

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

`x -> oo => 1/x -> 0`

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

= `((cos 0)^oo)^2`

= `1^2`

= 1

The limit `lim_(x->oo) ((cos (1/x))^x)^2 = 1`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes