Solution: In Exercises 67–72, use a CAS to estimate the
Chapter 3, Problem 69CE(choose chapter or problem)
In Exercises 67–72, use a CAS to estimate the magnitude of the error in using the linearization in place of the function over a specified interval \(l\). Perform the following steps:
a. Plot the function \(F\) over \(l\).
b. Find the linearization L of the function at the point a.
c. Plot \(f\) and \(L\) together on a single graph.
d. Plot the absolute error \(|f(x)-L(x)|\) and \(l\) find its maximum value.
e. From your graph in part (d), estimate as large a \(\delta>0\) as you can, satisfying
\(|x-a|<\delta \Rightarrow|f(x)-L(x)|<\epsilon\)
For \(\epsilon=0.5,0.1\), and \(0.01\). Then check graphically to see if your (\delta\)-estimate holds true.
\(f(x)=x^{2 / 3}(x-2), \quad[-2,3], \quad a=2\)
Equation Transcription:
Ƒ
ƒ
L
=0.5, 0.1
f(x) = x2/3 (x ⎯ 2), [⎯2, 3], a = 2
Text Transcription:
Ƒ
ƒ
L
|f(x) ⎯ L(x)|
delta>0
delta
|x-a<delta -> |f(x)-L(x)|<epsilon
epsilon=0.5, 0.1
f(x) = x^2/3 (x ⎯ 2), [⎯2, 3], a = 2
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer