The function f (x) = x-1 changes its value when x changes from xo to xo + dx. Let xo = 0.5 and dx = 0.1. %3D Find a. the change Af = f(xo + dx) – f(xo); b. the value of the estimate df = f'(xo) dx; and %3D c. the approximation error |Af – df|.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 2E
icon
Related questions
Question
The function f (x) = x-1 changes its value when x changes from xo to xo + dx. Let xo = 0.5 and dx = 0.1.
Find
a. the change Af = f(xo + dx) – f(xo);
b. the value of the estimate df = f'(xo) dx; and
%3D
%3D
c. the approximation error |Af – df|.
y = f(x)/
Af = f(xo + dx) - f(xo)
df = f'(xo) dx
dx
Tangent
Xo + dx
d) Write the linearization of f (x) at xo = 0.5.
Transcribed Image Text:The function f (x) = x-1 changes its value when x changes from xo to xo + dx. Let xo = 0.5 and dx = 0.1. Find a. the change Af = f(xo + dx) – f(xo); b. the value of the estimate df = f'(xo) dx; and %3D %3D c. the approximation error |Af – df|. y = f(x)/ Af = f(xo + dx) - f(xo) df = f'(xo) dx dx Tangent Xo + dx d) Write the linearization of f (x) at xo = 0.5.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Numerical Differentiation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning