# Horizontal asymptote question

1. Aug 18, 2004

### singleton

Well I'm going through an introductory calculus book and right now I'm on the section of horizontal asymptotes.

Currently I'm stubbed on this:
y = (x^2 - 1) / (x^2 + 1)

I take the limit of the function as x increases or decreases without bound and come up with y = 1 being the horizontal asymptote. No problem so far.

However, the book sketches it so that the curve is always above the asymptote for both + and - infinite.

The only problem is that if you substitute values for both sides, won't it ALWAYS be under the asymptote (since its a fraction less than one)? There will always be a value of 2 more on the denominator than the numerator.

So, am I right and the book wrong or what is what ;)

Last edited: Aug 18, 2004
2. Aug 18, 2004

### Muzza

Yeah, seems like the book is wrong.

3. Aug 18, 2004

### marlon

singleton,

i am also convinced your book is wrong

regards
marlon

4. Aug 18, 2004

### e(ho0n3

The book is wrong. What a strange book. Can you tell us what book it is?

5. Aug 18, 2004

### singleton

Calculus (MCA-OAF) by the education ministry of Ontario ;)

6. Aug 19, 2004

### HallsofIvy

Staff Emeritus
A math book written by an education ministry? That explains it!

(Probably, the picture got flipped at the printers.)

7. Aug 19, 2004

### singleton

It isn't just the picture ;) It describes it the same way heh.