Question

What is the limit of `(x^3 - 2x +3) / (5-2x^2)` as x goes to infinity?

Answer 1

`lim_(xrarroo) (x^3 - 2x +3) / (5-2x^2) = -oo`

Explanation:

`lim_(xrarroo) (x^3 - 2x +3) / (5-2x^2)` has indeterminate form `oo/oo`.

For all `x !=0` we get `(x^3 - 2x +3) / (5-2x^2)= (x^2(x-2/x+3/x^2))/(x^2(5/x^2-2))`

So
`lim_(xrarroo) (x^3 - 2x +3) / (5-2x^2) =lim_(xrarroo) (x-2/x+3/x^2)/(5/x^2-2) =oo/-2 = -oo`