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

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Answer 1 · 2015-10-23T20:26:45

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

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

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