How do you find oblique asymptote? (1 Viewer)

[enigma_1]

Apparently you use long division, but is there another way?

Thanks

 

[seanieg89]

Long division is the best way really.

 

[enigma_1]

hmm ok thanks! And when you do the long division, what exactly is the equation of the line? Does it include the remainder or do I omit that?

Eg after doing long division if I got 2x-1 r 3, then what is the equation of the oblique asymptote?

 

[seanieg89]

hmm ok thanks! And when you do the long division, what exactly is the equation of the line? Does it include the remainder or do I omit that?

Eg after doing long division if I got 2x-1 r 3, then what is the equation of the oblique asymptote?

No, the remainder is the thing you neglect. The point of long division is you can write:

p(x)/q(x) = f(x) + r(x)/q(x)

where r is your remainder and deg(r) < deg(q). Since q has higher degree than r, the ratio r/q tends to zero for large x, so p/q has an oblique asymptote f.

 

[rumbleroar]

You can also use the method where you add and take away stuff on the numerator to make it look similar to your denominator and divide, giving you a HA or OA. But I've heard it's a confusing method, so it depends what you're more comfortable with.