Originally Posted by

**rainer** $\displaystyle f(x)\equiv y$

The roots of y in the equation $\displaystyle y^2x^2+y(2x^2-1)+x^2-1=0$ (which is the equation plotted in the attachment)

are $\displaystyle -1$ and $\displaystyle \frac{1}{x^2}-1$

So, $\displaystyle \lim_{x\to\infty} y$ i.e. $\displaystyle \lim_{x\to \infty}\frac{1}{x^2}-1=-1$

(The limit was as x goes to infinity, not 0. REALLY SORRY about that.)

and yet the other root of y euals this limit, equals -1. So, can't it be said that the function y equals its limit?