We define the first difference of a function by (x) (x 1) (x) Calculate (x 3 ), (x 2 ), and (x) Then find a polynomial P of degree 3 such that P (x 1) 2 and P(0) 0 Conclude that P(n) 1 2 2 2 n 2 ...

Lets start by calculating the first differences of the given functions 1 x3 x3 x 13 x3 Expanding ...

We define the first difference of a function by (x) = (x +

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We define the first difference δ ƒ of a function ƒ by δ ƒ(x) = ƒ(x + 1) − ƒ(x).

Calculate δ(x³), δ(x²), and δ(x). Then find a polynomial P of degree 3 such that δP = (x + 1)²and P(0) = 0. Conclude that P(n) = 1² + 2² + · · · + n².

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Oct 24, 2023 06:07 AM

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We define the first difference of a function by (x) = (x +

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Calculus

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