How do you find the limit as x approaches positive infinity $((x^2)-2x+3)/(6-(3x^4))$ ?

Question

1448 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-02T17:33:28

We are going to seek the limits of the highest powers.

The limit of your equation is thus $lim((x²)/(-3x^4))$
$=lim((-x²)/(3x²*x²))$

We simplify by $x²$ :

$=lim((-1)/(3x²))$

And we know that $lim(3x²)$ is $+prop$
And dividing -1 by a number approaching $+prop$ makes it approch $0$ ( staying negative )

Thus : $lim((x²-2x+3)/(6-(3x^4)))=0$

How do you find the limit as x approaches positive infinity ((x^2)-2x+3)/(6-(3x^4))((x^2)-2x+3)/(6-(3x^4))?