To sketch: The graph of function
Answer to Problem 20RE
The horizontal asymptotes of the function f are
Explanation of Solution
Theorem used:
1. If
2. If
Definition used: Horizontal asymptote:
The line
Calculation:
Consider the function
The graph of
From the Figure 1, it is observed that
Consider the function
Simplify the terms of numerator,
Case 1: When
Take limit on the above expression
Since
Thus, the horizontal asymptote to f is
Case 2: When
Take limit on the above expression,
Since
So, the horizontal asymptote to f is
Thus, it has been verified that
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