Here is Newton's method as applied to the function x**2-y, for
the purpose of finding the square root of y.

Several people were rather excited about the prospect of seeing
this C code, so here it is.  I spoke with your calculus lecturer
this afternoon and he doesn't feel that there is any harm to his
assignment in my providing you with this code.  This might be a
disappointment!

But I kinda wish I weren't showing this yet.  I want to derive it.
This will happen in the next lecture, which will be the first
lecture of next week (Thursday or Friday) (in these Thurs -> Wed
weeks of ours).  (It would be Wednesday, but that's the midterm...)


Anyway, here's the C code:


double mysqrt(double y)  /* requires y > 0 */
{
    double x = y / 2;
    while (fabs(x * x - y) > 1e-10)
        x = (x + y / x) / 2;
    return x;
}