22. Let f(x) = (x – 1)² g(x) = e-2x and h(x) = 1 + In(1 – 2x) (a) Find the linearizations of f, g, and h at a = 0. What do you notice? How do you explain what happened? (b) Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain.
22. Let f(x) = (x – 1)² g(x) = e-2x and h(x) = 1 + In(1 – 2x) (a) Find the linearizations of f, g, and h at a = 0. What do you notice? How do you explain what happened? (b) Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
Hello, I need some help with this problem?
Transcribed Image Text:22. Let
f(x) = (x – 1)²
g(x) = e-2x
and
h(x) = 1 + In(1 – 2x)
(a) Find the linearizations of f, g, and h at a = 0. What do
you notice? How do you explain what happened?
(b) Graph f, g, and h and their linear approximations. For
which function is the linear approximation best? For
which is it worst? Explain.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning