Can you provide a formal proof for:
lim X^2 = 9
x->3
For all consider the quadratic .
By Descartes rule of signs this has exactly one positive root, which I will call , which depends only on (if you are not happy with Descartes rule of signs here you can find the positive root explicitly if you prefer).
Now suppose , then:
.
But:
so:
But by construction .
Hence we have proven that for all there exists a such that implies that , so we have proven that:
RonL