Concept explainers
To estimate: The value of
Answer to Problem 47E
The exact value of
Explanation of Solution
Use online graphing calculator and draw the graph of
From Figure 1 it is identified that curve approaches approximately 7 as x approaches ∞.
Find the exact value with the help of L’Hospital’s rule as follows.
Let,
Take natural logarithm on both sides,
Therefore,
Obtain the value of the function as x approaches
As x approaches
As x approaches
Thus,
Therefore, apply L’Hospital’s Rule and obtain the limit.
Thus,
So, the equation (2) becomes,
Thus, 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