Question

How do you find `lim sqrt(x+2)/(sqrt(3x+1)` as `x->oo`?

Answer 1

`= 1/sqrt(3)`

Explanation:

`lim_(x to oo) lim sqrt(x+2)/(sqrt(3x+1)`

`= lim_(x to oo) lim (sqrt(x) (sqrt(1+2/(sqrt x))))/(sqrt x (sqrt(3+1/(sqrt x)))`

`= lim_(x to oo) lim ( (sqrt(1+2/(sqrt x))))/( (sqrt(3+1/(sqrt x)))`

`= 1/sqrt(3)`