Concept explainers
(a)
To state: The L’Hospitals rule and explain.
(a)
Explanation of Solution
The L’Hospital’s rule:
“Suppose f and g are differentiable functions with
It states that if a limit of a quotient of a function is in an indeterminate form, then the limit of the quotient of the function is same as the limit of quotient of the derivatives subject to condition that all limits exist.
(b)
To explain: The use of L’Hospital’s rule for the limit of product of the functions fg such that
(b)
Explanation of Solution
Calculation:
Rearrange the given function in quotient form and then use the Quotient rule.
On further simplification,
So on applying L’Hospitals rule, it is easy to evaluate the given limit.
(c)
To explain: The use of L’Hospital’s rule for the limit of difference of the functions f
(c)
Explanation of Solution
Calculation:
Rewrite the given function as follows.
Use the sum rule and find the limit as follows,
On further simplification,
So on applying L’Hospitals rule, it is easy to evaluate the given limit.
(d)
To explain: The use of L’Hospital’s rule for
(d)
Explanation of Solution
Calculation:
Find the limit as follows.
The value of the above limit is in an indeterminate form.
So on applying L’Hospitals rule, it is easy to evaluate the given limit.
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