Consider the following function, f(x) = x³, 3 a = 1, n = 3, 0.8 ≤ x ≤ 1.2 (a) Approximate

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.2: Remainder And Factor Theorems
Problem 51PS
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Consider the following function,
f(x) = x ³₂
a = 1,
n = 3,
0.8 ≤ x ≤ 1.2
(a) Approximate
f(x)
by a Taylor polynomial with degree
n
at the number
a
Transcribed Image Text:Consider the following function, f(x) = x ³₂ a = 1, n = 3, 0.8 ≤ x ≤ 1.2 (a) Approximate f(x) by a Taylor polynomial with degree n at the number a
(b) Evaulate
f(1.1)
using the Tayor polynomial found in (a).
(c) Use Taylor's Inequality to estimate the
accuracy of the approximation
f(x) ≈ Tn(x)
when
X
lies in the given interval. (Round your
answer to six decimal places.)
Transcribed Image Text:(b) Evaulate f(1.1) using the Tayor polynomial found in (a). (c) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when X lies in the given interval. (Round your answer to six decimal places.)
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