Concept explainers
To evaluate: The limit of the function
Answer to Problem 9E
The limit of the function is 4.
Explanation of Solution
Limit Laws:
Suppose that c is a constant and the limits
Limit law 2:
Limit law 7:
Limit law 8:
Direct substitution property:
If f is a polynomial or a rational function and a is in the domain of f, then
Fact 1:
If
Calculation:
Compute the limit value of the denominator.
Since the limit of the denominator is zero, the quotient law cannot be applied.
Let
Simplify
Factorise the numerator
Substitute
Cancel the common terms from both the numerator and the denominator,
Use fact 1,
Apply direct substitution property on the limit function.
Thus, the limit of the function is 4.
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