Concept explainers
To evaluate: The value of
Answer to Problem 1P
The limit of the function is
Explanation of Solution
Result used:
Difference of squares formula:
Difference of cubes formula:
Direct substitution property:
If f is a polynomial or a rational function and a is in the domain of f, then
Calculation:
Obtain the limit of the function
Consider the function
Take the limit of the function as x approaches 1.
Let
On substitution,
Apply the difference of squares and cubes formulae in the numerator and the denominator as follows,
Thus, the limit of the function is
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