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Let y(x) = x3 for which (xo, yo), (x1,y1), (x2, y2) and (x3, y3) are given by k 0 1 2 3 Xk 0.1 1.0 4.0 6.0 -19 -29 Ук 500 -4.0 64 216 (c) Use a first order Taylor series expansion to approximate the functional value at x = 6.1. As expansion point of the series use x3 = 6.0. In addition, for an approximation of y'(x3) use the backward difference quotient at position x3, y(x3) - y(x2) i.e. y'(x3) ≈ Do not use the analytical derivative! Determine X3 - X2 • the relative error with respect to the exact value y(6.1).

Let y(x) = x3 for which (xo, yo), (x1,y1), (x2, y2) and (x3, y3) are given by k 0 1 2 3 Xk 0.1 1.0 4.0 6.0 -19 -29 Ук 500 -4.0 64 216 (c) Use a first order Taylor series expansion to approximate the functional value at x = 6.1. As expansion point of the series use x3 = 6.0. In addition, for an approximation of y'(x3) use the backward difference quotient at position x3, y(x3) - y(x2) i.e. y'(x3) ≈ Do not use the analytical derivative! Determine X3 - X2 • the relative error with respect to the exact value y(6.1).

Advanced Engineering Mathematics
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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Let y(x) = x3 for which (xo, yo), (x1,y1), (x2, y2) and (x3, y3) are given by k 0 1 2 3 Xk 0.1 1.0 4.0 6.0 -19 -29 Ук 500 -4.0 64 216
Transcribed Image Text:Let y(x) = x3 for which (xo, yo), (x1,y1), (x2, y2) and (x3, y3) are given by k 0 1 2 3 Xk 0.1 1.0 4.0 6.0 -19 -29 Ук 500 -4.0 64 216
(c) Use a first order Taylor series expansion to approximate the functional value at x = 6.1. As expansion point of the series use x3 = 6.0. In addition, for an approximation of y'(x3) use the backward difference quotient at position x3, y(x3) - y(x2) i.e. y'(x3) ≈ Do not use the analytical derivative! Determine X3 - X2 • the relative error with respect to the exact value y(6.1).
Transcribed Image Text:(c) Use a first order Taylor series expansion to approximate the functional value at x = 6.1. As expansion point of the series use x3 = 6.0. In addition, for an approximation of y'(x3) use the backward difference quotient at position x3, y(x3) - y(x2) i.e. y'(x3) ≈ Do not use the analytical derivative! Determine X3 - X2 • the relative error with respect to the exact value y(6.1).
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