How do you find horizontal asymptotes in calculus?

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- anonymous

How do you find horizontal asymptotes in calculus?

- schrodinger

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- amistre64

Hmmm.... i dont quite know what you are asking. Asymptotes tend to be stationary, and calulus deals with movement. "HA"s are found from the original function and tend to be limits of the function.

- anonymous

Say for the question 2x/(x^2+9), what is the "calculus method" of getting the H.A.? There is something in my notes about dividing by the largest power and dividing the numerator by the denominator.

- amistre64

Dividing by the largest power is the algebra way.
In calculus, you can derive another equation from the original to tell you how the original is affected by change; but that does not effect the "HA"s of the original equation in any way, nor does it help you to find them.
For example, the HA of 2/x is y=0. But the derivative of (2/x) is -2/x^2 which doesnt help in finding the HA.

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- anonymous

Ok thanks!
I have this example too that didn't make much sense:
x+1 (divide by x)
lim ----
x->infinite x-2 (divide by x)
1+1/x -->0
= lim -----
1 - 2/x -->0
H.A. = 1

- anonymous

Wait.. I know what its getting at but still.....

- amistre64

There are 3 simple rules for finding HAs, but they are not calculus. They are just generalizations after doing quite a few algebra modifications.

- amistre64

If the highest power of x is in the bottom; then the HA =0
If the highest power of x is the same in the top and bottom, the HA=the leading coeficients: example, 5x^2/7x^2. HA=5/7
If the highest power of x is found in the top; then the asymptote is a line or curve and not horizontal

- anonymous

Ah that helps me out alot! Thank you for helping me :D

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