Find `lim_(x->oo)root(3)((7x^2+9x+6)/(27x^2+1))` :

`lim_(x->oo)root(3)((7x^2+9x+6)/(27x^2+1))`

`=root(3)(lim_(x->oo)(7x^2+9x+6)/(27x^2+1))`

`=root(3)(lim_(x->oo)(7+9/x+6/x^2)/(27+1/x^2))`

`=root(3)(7/27)`

`=root(3)(7)/3~~.637643728`

Find `lim_(x->oo)root(3)((7x^2+9x+6)/(27x^2+1))` :

`lim_(x->oo)root(3)((7x^2+9x+6)/(27x^2+1))`

`=root(3)(lim_(x->oo)(7x^2+9x+6)/(27x^2+1))`

`=root(3)(lim_(x->oo)(7+9/x+6/x^2)/(27+1/x^2))`

`=root(3)(7/27)`

`=root(3)(7)/3~~.637643728`