Use the Remainder Estimation Theorem to find an interval containing x=0 over which f(x) can be approximated by p(x) to three decimal-place accuracy throughout the interval.
f(x)=cosx p(x)=1 - x^2/2! + x^4/4!
We set the term less then the error (x and all)
and solve the inequality for x. This gives us the distance x can be from the center of the series and get the accuracy we want. The Series is centered at zero.
since we get the set
lets do a quick check
p(.65)=.796187
cos(.65)=.79608
The error is within what we wan't yeah!!