Approximate the function f (x) = sin(e*) about x = a = 1.5 %3D Using the Taylor expansion until P3 (evaluating 4 terms Po, P1, P2, P3) Graph each Taylor Polynomial (Po, pP1,P2, P3) in a single plotting area For each Taylor Polynomial (po, P1, P2, P3) approximate f(x) at x = 1.75 Compare and compute the error from the theoretical value of sin(e1.75) = -0.50431 For each Taylor Polynomial (po, P1, P2, P3)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Problem 1:
Approximate the function
f (x) = sin(e*) about x = a = 1.5
Using the Taylor expansion until p3
(evaluating 4 terms Po, P1, P2, P3)
f(x) = sin(o(*))
0.5
Graph each Taylor Polynomial (Po,P1, P2, P3)
in a single plotting area
-0.5
0.5
1.5
-0.5
For each Taylor Polynomial (Po, P1, P2, P3)
approximate f(x) at x
1.75
Compare and compute the error from the
theoretical value of sin(e1.75) = -0.50431
For each Taylor Polynomial (Po, P1, P2, P3)
-1:5
Error = (absolute error) = abs (theoretical – computed)
! Use RADIANS mode in your calculator
! Take note of the PRODUCT and CHAIN RULES of differentiation
Transcribed Image Text:Problem 1: Approximate the function f (x) = sin(e*) about x = a = 1.5 Using the Taylor expansion until p3 (evaluating 4 terms Po, P1, P2, P3) f(x) = sin(o(*)) 0.5 Graph each Taylor Polynomial (Po,P1, P2, P3) in a single plotting area -0.5 0.5 1.5 -0.5 For each Taylor Polynomial (Po, P1, P2, P3) approximate f(x) at x 1.75 Compare and compute the error from the theoretical value of sin(e1.75) = -0.50431 For each Taylor Polynomial (Po, P1, P2, P3) -1:5 Error = (absolute error) = abs (theoretical – computed) ! Use RADIANS mode in your calculator ! Take note of the PRODUCT and CHAIN RULES of differentiation
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