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Let τ(X) be the Taylor Series expansion of f(x) = x3 + x2 + 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?

Let τ(X) be the Taylor Series expansion of f(x) = x3 + x2 + 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? Correct Answer 1770

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

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