In the final part of 3d, we are required to find the maximum number of terms to keep the absolute value of the remainder below 10^(-16) for any x.
But shouldn’t we find the minimum number of terms instead? For example , if n is really big, the remainder is sure to be very small ( and it becomes even smaller when n gets bigger and bigger)
Yes, I have rephrased to
What is the minimum number of terms (or what is the minimum $n$)
that, for any $x$, no matter how large,
guarantees to keep the absolute value of the remainder
$|R_{2n+2} |$ below $10^{-16}$?
So minimum terms, but even for max x.