Concept explainers
To illustrate: L’Hospitals rule by ploting
Answer to Problem 49E
The exact value of
Explanation of Solution
Given:
The functions are
Calculation:
The value of
The value of,
Use the online graphing calculator and draw the graph of
From Figure 1, it is identified that both curves approaches 0.25 as x approaches 0. Thus,
Find the exact limit as follows.
Obtain the value of the function as x approaches
As x approaches 0, the numerator is,
As x approaches 0, the denominator is,
Thus,
Therefore, apply L’Hospital’s Rule and obtain the limit.
Thus,
Therefore, the exact value of
Chapter 4 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