To Verify: The given function is continuous and state the domain. State the theorem
used and the function that assumed to be continuous.
Answer to Problem 38E
The given function is continuous and it is verified by using the sum theorem,
composite theorem and product theorems.
The domain is
Explanation of Solution
Given:
Calculation:
Given the function
Here
By using the sum theorem:
Substitute
Thus the function
By using the composite theorem,
Substitute
Thus the function
And by using the product theorem:
Substitute
Thus the function
And by using the sum theorem:
Substitute
Thus the function
Find Domain:
The domain of the expression is all real numbers except where the expression is
undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
Thus, the domain of the function is
Chapter 1 Solutions
CALCULUS-W/XL ACCESS
- 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