Concept explainers
Evaluate the limit, if it exists.
To evaluate: The limit of the function
Answer to Problem 10E
The limit of the function is
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
Factorize the numerator
Substitute
Take the common terms out from the numerator,
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
Chapter 2 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
Additional Math Textbook Solutions
Precalculus: A Unit Circle Approach
Thomas' Calculus: Early Transcendentals (14th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Calculus: Early Transcendentals (2nd Edition)
Calculus For The Life Sciences
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning