Question

How to solve `lim_(x->oo)( sqrt(x^3+x) - root(3)(x^2+1))` ?

Answer 1

`oo`

Explanation:

`( sqrt(x^3+x) - root(3)(x^2+1)) = x^(3/2)sqrt(1+1/x^2)-x^(2/3)root(3)(1+1/x^2) = x^(3/2)(sqrt(1+1/x^2)-x^-(5/6)root(3)(1+1/x^2))` then

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