2. The position of a water particle flowing in a tube at the Water Treatment Facility is given by the function of time: f(t)=25t³-6t² + 7t-88 Use zero- through third-order Taylor series expansions to predict the position of the water particle at 3 seconds f(3) using a base point at t = 1. Compute the true percent relative error for each approximation.
2. The position of a water particle flowing in a tube at the Water Treatment Facility is given by the function of time: f(t)=25t³-6t² + 7t-88 Use zero- through third-order Taylor series expansions to predict the position of the water particle at 3 seconds f(3) using a base point at t = 1. Compute the true percent relative error for each approximation.
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:2. The position of a water particle flowing in a tube at the Water Treatment Facility is given by the
function of time:
f(t) = 25t³ - 6t² +7t-88
Use zero- through third-order Taylor series expansions to predict the position of the water particle
at 3 seconds f(3) using a base point at t = 1. Compute the true percent relative error for each
approximation.
Expert Solution
Step 1
Taylor's series is used for the expansion of the function. The Taylor's series is,
.
zeroth order is,
The first order is,
.
The second order is,
.
The third order is,
.
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