What is Peano error?
Here in America it is called "Lagrange's Remainder".
But, I do not think you need to include that. Just express the polynomial and ignore the remainder term (which hopefully is a very small number).
if i'm asked to find the third order maclaurin polyn. of a function i have to stop at the third order without including peano's error(which would mean writing the complete maclaurin polynomial), right? for instance f(x)=e^(x^2)+x^3 M3=1+x^2 + x^3 without +o(x^3)