`lim_(x->oo)x^3/(x+2)` Evaluate the limit, using L’Hôpital’s Rule if necessary.

Given to solve,

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

as `x->oo` then the `x^3/(x+2) =oo/oo` form

so upon applying the L 'Hopital rule we get the solution as follows,

If

`lim_(x->a) f(x)/g(x) = 0/0` or `(+-oo)/(+-oo)` then by using the L'Hopital Rule we get  the solution with the  below form.

`lim_(x->a) (f'(x))/(g'(x))`

so , now evaluating

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

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

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

by plugging the value `x=oo` , we get

=` 3(oo)^2`

= `oo`