How can you tell when an equation has an oblique asymptote? (1 Viewer)

[trolol101]

Something something about powers.

 

[Carrotsticks]

Something something about powers.

 

[QZP]

^ Adding on, I believe it is only strictly correct to refer to asymptotes as straight lines. Thus you have an oblique asymptote when deg (A) - deg (B) = 1. Otherwise, the function is asymptotic to y = x^2, say.

 

[Drongoski]

Yep, qzp. When C(x) is linear.

 

[Carrotsticks]

^ Adding on, I believe it is only strictly correct to refer to asymptotes as straight lines. Thus you have an oblique asymptote when deg (A) - deg (B) = 1. Otherwise, the function is asymptotic to y = x^2, say.

EDIT: Correct, thank you. I mis-took 'oblique' to be 'non-horizontal asymptotes'.

However, I would like to point out that asymptotes can be curves, sometimes called 'curvilinear asymptotes'.

But oblique asymptotes must be in the form y=mx+b, where m is non-zero.

 

[trolol101]

I don't understand that second paragraph...

 

[asianese]

deg: degree - i.e. the highest power of the polynomial.

e.g. 2x^4 + 4x has degree 4, since the highest power is 4.

 

[braintic]

^ Adding on, I believe it is only strictly correct to refer to asymptotes as straight lines. Thus you have an oblique asymptote when deg (A) - deg (B) = 1. Otherwise, the function is asymptotic to y = x^2, say.

Asymptotes don't have to be straight lines.

Wolfram definition: An asymptote is a line or curve that approaches a given curve arbitrarily closely.

It IS correct to say that y=x^2 is an asymptote of y=x^2 + 1/x.