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`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`

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