Concept explainers
The domain of the function.
Answer to Problem 63E
The domain of the function will be all real values of
Explanation of Solution
Given:
The right angled triangle in first quadrant with base
Formula used:
The area of right angled triangle, A is
Calculation:
Consider following right angled triangle in first quadrant with base
Aline is passing through coordinate (2, 1).
A right angled triangle with base x and height y as there are infinite lines passing through point (2, 1).
The area of right angled triangle, A is
Now determining the functionof A in terms of X.
Making to get y in terms ofX
The slope of a line is
Slope of line with coordinates
Slope of line with coordinates
Thus, we get
This is the required answer.
Now, finding the domain of above function as,
As the right angled triangle is in first quadrant, then X can only takes positive values, that is
It includes only those values in the domain where denominator is non-zero.
For x=2, the denominator becomes zero.
So, exclude x=2
Hence, the domain of this function is all real values of
Conclusion:
The domain of the function will be all real values of
Chapter 1 Solutions
EBK PRECALCULUS W/LIMITS
- 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