# How to find oblique Asymptote

• Mar 27th 2009, 04:40 AM
supersaiyan
How to find oblique Asymptote
How do you find the oblique asymptote of 2X^2/ X-4
• Mar 27th 2009, 04:48 AM
stapel
Quote:

Originally Posted by supersaiyan
How do you find the oblique asymptote of 2X^2/ X-4

To find oblique (or "slant") asymptotes, do the polynomial long division:

[html] 2x + 8
----------------
x - 4 ) 2x^2 + 0x + 0
2x^2 - 8x
----------------
8x + 0
8x - 32
----------------
32[/html]
So the slant asymptote will be y = 2x + 8. :D
• Mar 27th 2009, 01:24 PM
supersaiyan
Thanks, that what I thought but my teacher said it's just 2X
• Mar 28th 2009, 10:42 AM
stapel
Quote:

Originally Posted by supersaiyan
Thanks, that what I thought but my teacher said it's just 2X

Graph the function and look. Does the slant asymptote appear to pass through the origin, or not? (Make sure you "zoom out" on the graph, so you can see what's going on off to the sides. The slanty trend of the curve does not correspond to a line through the origin!) (Wink)
• Mar 28th 2009, 04:06 PM
mr fantastic
Quote:

Originally Posted by supersaiyan
Thanks, that what I thought but my teacher said it's just 2X

If the equation is $\displaystyle y = \frac{2x^2}{x} - 4$ then your teacher is correct.

If the equation is $\displaystyle y = \frac{2x^2}{x - 4}$ then your teacher is wrong.