- (a) The table below is constructed from the information given in Question 5 in BC Practice Exam
Three.
n f (n) (5)0 2 2
1 −2 −2
2 −1
3 6 1
(c) Use Taylor’s theorem around x = 0.n g(n)(x) g(n)(0)0 f (2x + 5) f (5) = 2 21 2 f′ (2x + 5)^2 f′ (5) = 2(−2) =−4 −42 4 f ′′ (2x + 5)^4 f^ ′′ (5) = 4(−1) =−4 −23 8 f′′′(2x + 5)^8 f′′′(5) = 8(6) = 48 8g(x) ≈ 2 − 4x − 2x^2 + 8x^3.