Question

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

Answer 1

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

• For the numerator :
  The highest power is `x²`
• For the denominator :
  The highest power is `-3x^4`

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`