The question is as follow:
(a) The first three Chebyshev polynomials are: $$T_0=1$$ $$T_1 = x$$ $$T_2 = 2x^2-1$$ $$T_3 = 4x^3-3x$$ $$T_4 = 8x^4-8x^2+1$$
i) Economize the truncated power series: $$p(x)=1+2x−x^3+3x^4$$
ii) Give the upper limit for the absolute value of the difference between the original truncated power series and the economized one.
My question relates to (ii). After economizing the given power series using Chebyshev polynomials, do I simply test values of $x$ in $[-1,1]$ using both the original and economized series and then determine the maximum error which would then be the upper limit/bound?