Use a CAS to estimate the magnitude of the error in using the linearization in place of

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Use a CAS to estimate the magnitude of the error in using the linearization in place of the function over a specified interval I. Perform the following steps:


a. Plot the function ƒ over I.


b. Find the linearization L of the function at the point a.


c. Plot ƒ and L together on a single graph.


d. Plot the absolute error |ƒ(x) - L(x)| over I and find its maximum value.


e. From your graph in part (d), estimate as large a δ > 0 as you can, satisfyingimage


for ϵ = 0.5, 0.1, and 0.01. Then check graphically to see if your δ-estimate holds true.


ƒ(x) = √x - sin x, [0, 2π], a = 2

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Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

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