Question

Let τa(f(x)) denote the Taylor series of the polynomial f(x) centered at a. Which of the following exactly happens after the Taylor series is formed?

(a) τa(f(x)) = f(x)

(b) The Taylor series has the effect of scaling GRAPH OF f(x)

(c) The Taylor series transforms the origin

(d) Scaled up graph obtained by factor of a

I have been asked this question in unit test.

I'm obligated to ask this question of Taylor Mclaurin Series topic in portion Differential Calculus of Engineering Mathematics

Answer 1

Correct answer is (a) τa(f(x)) = f(x)

Easiest explanation: The Taylor series has no effect whatsoever on the nature of the polynomial. This is because the Taylor series is itself a polynomial and hence no change takes place.

τa(f(x)) = f(x).