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Calculus / Calculus: Early Transcendentals 3 / Chapter 8.4 / Problem 54

Calculus: Early Transcendentals | 3rd Edition | ISBN: 9781464114885 | Authors: Jon Rogawski, Colin Adams

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Let Tn be the nth Taylor polynomial at x = a for a polynomial f of degree n. Based on

Chapter 8, Problem 54

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QUESTION:

Let \(T_{n}\) be the nth Taylor polynomial at x = a for a polynomial f of degree n. Based on the result of Exercise 53, guess the value of \(\left|f(x)-T_{n}(x)\right|\). Prove that your guess is correct using the error bound.

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QUESTION:

Let \(T_{n}\) be the nth Taylor polynomial at x = a for a polynomial f of degree n. Based on the result of Exercise 53, guess the value of \(\left|f(x)-T_{n}(x)\right|\). Prove that your guess is correct using the error bound.

ANSWER:

Step 1 of 3

The Taylor polynomial \(T_{n}(x)\) of a polynomial f of degree is exactly equal to f. It just might look different if not centered at 0 , but if you were to simplify it would become the exact same.

So then the error bound must be \(0\)

\(\left|f(x)-T_{n}(x)\right|=0\)

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