Concept explainers
b.
To check:whether the given function f has a removable discontinuity at a . if the discontinuity is removable, then find a function g that agrees with f for
b.
Answer to Problem 37E
Removable discontinuity.
Explanation of Solution
Given:
The given function is
Calculation:
The given function is
f can be extended to a continuous function on
Define
Then g is defined and continuities for all real numbers and
Therefore,
b.
To check: whether the given function f has a removable discontinuity at a . if the discontinuity is removable, then find a function g that agrees with f for
b.
Answer to Problem 37E
Removable discontinuity.
Explanation of Solution
Given:
The given function is
Calculation:
The given function is
f can be extended to a continuous function on
Define
Then g is defined and continuities for all real numbers and
Therefore,
c.
To check: whether the given function f has a removable discontinuity at a . if the discontinuity is removable, then find a function g that agrees with f for
c.
Answer to Problem 37E
Jump discontinuity and non-removable.
Explanation of Solution
Given:
The given function is
Calculation:
The given function is
Remember that x is the “greatest integer” function, which equals the largest not integer not greater than x .
For
TFor
Thus,
Chapter 2 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning