Concept explainers
To determine: Whether the statement is true or false.
In a parameterization, if x is a continuous function of t and y is a continuous function of t , then y is a continuous function of x .
Answer to Problem 45E
The given statement is false.
Explanation of Solution
Calculation:
It is known that in a parameterization, if x and y are two continuous functions of t ; then the functions can be written as:
Here, g and h are continuous functions.
Rewrite the equation (1) as:
Substitute
The functions
And,
This means that y is not a continuous of x .
Hence, the given statement is false.
Chapter 11 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus & Its Applications (14th Edition)
Calculus: Early Transcendentals (2nd Edition)
University Calculus: Early Transcendentals (3rd Edition)
Calculus and Its Applications (11th 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