Question

How do you evaluate the limit `x/(sqrt(3x^2+1)` as x approaches `oo`?

Answer 1

`1/sqrt3`

Explanation:

Let `L = lim_(x->oo) x/(sqrt(3x^2+1))`

`= lim_(x->oo) (x/x)/(1/x(sqrt(3x^2+1)))`

`= lim_(x->oo) 1/sqrt((1/x^2(3x^2+1)))`

`= lim_(x->oo) 1/sqrt((3 + 1/x^2))`

`= 1/(sqrt(3+0)) = 1/sqrt3`