Consider the following function. f(x) = sin(x), a = ₁ n = 4, 0≤x≤ (a) Approximate f by a Taylor polynomial with degree n at the number a. (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) x T (x) when x lies in the given interval. (Round your answer to six decimal places.) IR₂(X)IS (c) Check your result in part (b) by graphing IR,(x). y 0.0005 0.0004 0.0003 0.0002 0.0001 O 0.2 0.4 0.6 0.8 1.0 X y -0.0001 -0.0002 -0.0003 -0.0004 -0.0005 0.2 94 0.6 0.8 T 1.0 X y -0.0001 -0.0002 -0.0003 -0.0004 -0.0005 0.2 0.4 0.6 0.8 1.0 X 0.0005 0.0004 0.0003 0.0002 0.0001 0.2 0.4 0.6 0.8 1.0 y
Consider the following function. f(x) = sin(x), a = ₁ n = 4, 0≤x≤ (a) Approximate f by a Taylor polynomial with degree n at the number a. (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) x T (x) when x lies in the given interval. (Round your answer to six decimal places.) IR₂(X)IS (c) Check your result in part (b) by graphing IR,(x). y 0.0005 0.0004 0.0003 0.0002 0.0001 O 0.2 0.4 0.6 0.8 1.0 X y -0.0001 -0.0002 -0.0003 -0.0004 -0.0005 0.2 94 0.6 0.8 T 1.0 X y -0.0001 -0.0002 -0.0003 -0.0004 -0.0005 0.2 0.4 0.6 0.8 1.0 X 0.0005 0.0004 0.0003 0.0002 0.0001 0.2 0.4 0.6 0.8 1.0 y
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) = sin(x),
(a) Approximate f by a Taylor polynomial with degree n at the number a.
T4(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 six decimal places.)
IR₂(x)| ≤
(c) Check your result in part (b) by graphing IR,(x)\.
y
0.0005
0.0004
π
a=-1 n = 4, osxs
6
X
0.8
1.0
-0.0001
-0.0002
UTAU
-0.0003
-0.0004
0.0003
0.0002
0.0001
0.2
IT
0.4
0.6
0.8
1.0
X
y
-0.0001
-0.0002
-0.0003
-0.0004
-0.0005
0.2 04 0.6
y
-0.0005
0.2 0.4
0.6
0.8
1.0
y
X
0.0005
0.0004
0.0003
0.0002
0.0001
0.2
0.4
0.6
0.8
1.0
X
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