Using differentials to approximate the value of an expression.

Question

Use differentials to approximate the value of the expression. Compare your answer with that of a calculator. (Round your answers to four decimal places.)

(2.99)^3

Using differentials _____________________

Using calculator _______________________

Answer 1

Let f(x) = x³; Δf = f(2.99) - f(3); f(2.99) = f(3) + Δf ≈ 3³ + df = 27 + f'(3)·Δx = 27 + 3·3²(2.99 - 3) = 27 - 0.27 =

26.73

With calculator: 2.99³ = 26.7309