as x gets large, f(x) ≈ x^4/x^2 = x^2
so f(x) -> +∞
Give the rational function f(x)=x^4+2x^3-4x^2+8x+5/x^2+5x+6
What is the limits as x is going toward - infinity f(x)=?
I did x^4/x^2=x^2/X=X/1 so I got one as my answer.
Is this correct?
Thank you for checking my work.
3 answers
a little confused about that, but thank you for your help and checking over my work.
as x -> ∞, the high powers grow so much faster than the lower powers that they become effectively zero, so you can ignore them.
Alternatively, divide top and bottom by x^2, That gives you
(x^2+2x-4 + 8/x + 5/x^2) / (1 + 5/x + 6/x^2)
Now, you know that 1/x and 1/x^2 both -> 0 as x ->∞
So the fraction becomes effectively
(x^2+2x-4)/1
which, of course, -> ∞ as x does.
Alternatively, divide top and bottom by x^2, That gives you
(x^2+2x-4 + 8/x + 5/x^2) / (1 + 5/x + 6/x^2)
Now, you know that 1/x and 1/x^2 both -> 0 as x ->∞
So the fraction becomes effectively
(x^2+2x-4)/1
which, of course, -> ∞ as x does.
2 answers