Consider the following function. f(x) = x¹/3, a = 1, n = 3, 0.8 ≤ x ≤ 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x)= T(x) when x lies in the given interval. (Round your answer to eight decimal places.) |R3(x)| ≤ (c) Check your result in part (b) by graphing IR(X)I. y 0.00012 0.00010 0.00008 0.00006 0.00004 0.00002 y -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 -0.00012 0.9 0.9 1.0 1.0 1.1 1.1 1.2 1.2 X X y 0.00012 0.00010 0.00008 0.00006 0.00004 0.00002 0.9 -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 -0.00012 1.0 1.1 0.9 M 1.1 1.2 1.2 X X
Consider the following function. f(x) = x¹/3, a = 1, n = 3, 0.8 ≤ x ≤ 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x)= T(x) when x lies in the given interval. (Round your answer to eight decimal places.) |R3(x)| ≤ (c) Check your result in part (b) by graphing IR(X)I. y 0.00012 0.00010 0.00008 0.00006 0.00004 0.00002 y -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 -0.00012 0.9 0.9 1.0 1.0 1.1 1.1 1.2 1.2 X X y 0.00012 0.00010 0.00008 0.00006 0.00004 0.00002 0.9 -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 -0.00012 1.0 1.1 0.9 M 1.1 1.2 1.2 X X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the following function.
f(x) = x¹/3, a = 1, n = 3,
(a) Approximate f by a Taylor polynomial with degree n at the number a.
T3(x) =
(b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x)= T(x) when x lies in the given interval. (Round
your answer to eight decimal places.)
|R3(x)| ≤
(c) Check your result in part (b) by graphing IR,(x)|.
y
0.00012
0.00010
0.00008
0.00006
0.00004
0.00002
y
-0.00002
-0.00004
-0.00006
-0.00008
-0.00010
-0.00012
0.9
0.9
0.8 ≤ x ≤ 1.2
1.0
1.0
1.1
1.1
1.2
1.2
X
X
y
0.00012
0.00010
0.00008
0.00006
0.00004
0.00002
y
-0.00002
-0.00004
-0.00006
-0.00008
-0.00010
0.00012
0.9
0.9
1.0
1.1
1.1
1.2
1.2
X
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