Homework Help

Given `lim_(x->6) f(x)=3` and `lim_(x->6) g(x)=7` , evaluate `lim_(x->6)...

user profile pic

jjmgingrich | Student, Undergraduate | Salutatorian

Posted January 20, 2013 at 3:22 PM via web

dislike 1 like

Given `lim_(x->6) f(x)=3` and `lim_(x->6) g(x)=7` , evaluate `lim_(x->6) sqrt(f(x))`

1 Answer | Add Yours

user profile pic

tiburtius | High School Teacher | (Level 3) Associate Educator

Posted January 20, 2013 at 3:47 PM (Answer #1)

dislike 1 like

Limit and continous function are commutative, that is if `c` is continous at `x_0` then `lim_(x->x_0) c(f(x))=c(lim_(x->x_0) f(x))`. Now since square root is continous at 6 it follows that

`lim_(x->6)sqrt(f(x)) = sqrt(lim_(x->6)f(x)) = sqrt(3)`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes