Question

How do you find the limit of `(1-2x^2-x^4)/(5+x-3x^4)` as `x->-oo`?

Answer 1

The limit is `y=1/3`

Explanation:

Rearranging the terms of the expression

`(1-2x^2-x^4)/(5+x-3x^2)=(-x^4-2x^2+1)/(-3x^4+x+5)`
As both numerator and denominator are polynomials, we take the highest degree
limit`=(-x^4)/(-3x^4)=1/3`
`x->-oo`
graph{(y-(-x^4-2x^2+1)/(-3x^4+x+5))(y-1/3)=0 [-5.546, 5.55, -2.77, 2.777]}