If f(x) = 1 + 3x - 5x^2 + 4x^3, which of the following are true statements?

Question

I. The Taylor polynomial of degree 3 about x = 3 for f(x) is equal to f(x).
II. The remainder term R5(x) for f(x) is equal to zero.
III. The remainder term R2(x) for f(x) is equal to zero.

a). I only
b). I and III only
c). I and II only
d). I, II, and III

Answer 1

a little reflection should convince you that C is the answer.
f(x) is a degree 3 polynomial, so all terms after the 4th are zero.