singleton
Aug18-04, 03:25 PM
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 ;)
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 ;)