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, satisfying

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

Transcribed Image Text:

|xa| < 8 11 |f(x) = L(x) < € -