How would I find the horizontal asymptote of this function?

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- Mar 9th 2011, 08:15 PMyoungb11Horizontal asymptote of this function

How would I find the horizontal asymptote of this function? - Mar 9th 2011, 08:26 PMTheChaz
This is ugly, but might be the best way....

(Considering "the bottom" to be "1")

Multiply top and bottom by the conjugate ...

Then you'll have 3x on top. As , the bottom will become closer to just

So we're looking at 3x over 2x --> 3/2.

Yeah... I'm betting soroban can do it more elegantly! - Mar 9th 2011, 08:32 PMyoungb11
- Mar 9th 2011, 09:05 PMSoroban
Hello, youngb11!

Thanks for the compliment, Chaz!

This is definitely not elegant, but it is more algebraically complete.

Quote:

We want: . .if it exists.

As TheChaz suggested, multiply top and bottom by the conjugate:

. .

. .

Divide top and bottom by

. .

. .

. . . . . . . . . .

- Mar 9th 2011, 09:06 PMyoungb11
Thanks a lot! And yes that was very elegant:p Very easy to understand thanks again!

- Mar 9th 2011, 09:10 PMTheChaz
I'm just wondering how you

*saw*the thread so quickly! (Of course, I'm also surprised/terrified by your answers from time to time ;) )