How do you find horizontal asymptotes in calculus?
Stacey Warren - Expert brainly.com
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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.
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.
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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I have this example too that didn't make much sense:
x+1 (divide by x)
x->infinite x-2 (divide by x)
= lim -----
1 - 2/x -->0
H.A. = 1
Wait.. I know what its getting at but still.....
There are 3 simple rules for finding HAs, but they are not calculus. They are just generalizations after doing quite a few algebra modifications.
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
Ah that helps me out alot! Thank you for helping me :D