Question

Just a quick question about oblique asymptotes. My lesson never taught me how to know if there is no oblique asymptotes, it just told me how to find them. How can I tell whether or not there are oblique asymptotes?

Answer 1

if the degree of the numerator is larger than the degree of the denominator by 1

Answer 2

for example
\[\frac{x^2-2x+3}{x-2}\] will have an "oblique" or "slant " asymptote

Answer 3

having a little typing problem here
if you divide a polynomial of degree n by a polynomial of degree n-1 you get a polynomial of degree 1, which is a line

Answer 4

Okay, so if there is no Horizontal Asymptote, there are no Oblique asymptote. Since there is no horizontal asymptote if you have a larger degree on the top. Correct?

Answer 5

if there is no horizontal asymptote, there may be an oblique asymptote
if there is a horizontal asymptote, then there is no oblique one

Answer 6

if the degree of the denominator is larger than the degree of the numerator, like in
\[\frac{x}{x^2-4}\] then the horizontal asymptote is \(y=0\)

Answer 7

sorry to interrupt, but could you help me here after, satellite
http://openstudy.com/study#/updates/546ab56fe4b0ecc32148b447

Answer 8

if the degrees are the same, as in '
\[\frac{2x^2+2}{3x^2+3x+4}\] then it is the ratio of the leading coefficients, in that case for example it would be \(y=\frac{2}{3}\)

Answer 9

Okay, that makes sense. My lesson explained that, it just wasn't very clear. Thanks for clearing everything up for me.