Question

Let τ(X) be the Taylor Series expansion of f(x) = x^3 + x^2 + 1019 centered at a = 1019, then what is the value of the expression 2(τ(1729))^2 + τ(1729) * f(1729) – 3(f(1729))^2 + 1770?

(a) 1770

(b) 1729

(c) 0

(d) 1

The question was asked in unit test.

The above asked question is from Taylor Mclaurin Series in division Differential Calculus of Engineering Mathematics

Answer 1

Right option is (a) 1770

Easy explanation: Observe first off that the given function is a polynomial and so any other representation (Taylor Series here) which is continuous and differentiable has to be the

same polynomial. This gives us

τ(x) = f(x)

We now evaluate the expression as follows

= 2(f(1729))^2 + (f(1729))^2 – 3(f(1729))^2 + 1770

= 3(f(1729))^2 – 3(f(1729))^2 +1770

= 1770