`lim_(x -> oo) (x + 1)/(x^2 + 1)^(1/3)` Find the limit.

Expert Answers
gsarora17 eNotes educator| Certified Educator

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

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

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

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

apply infinity properties,

`((1+0)oo)/root(3)(0+1)`

= `oo`