Concept explainers
a.
To make: a table of approximate values of
a.
Answer to Problem 41E
Convergent.
Explanation of Solution
Given information:
Calculation:
t | 2 | 5 | 10 | 100 | 1000 | 10000 |
f (t) | 0.447453 | 0.577101 | 0.621306 | 0.668479 | 0.672957 | 0.673407 |
From the table data, the integral
b.
To show: the
b.
Answer to Problem 41E
Explanation of Solution
Given information :
Formula used:
Comparison property for integrals:
If
Calculation:
Recall that
Hence proved that the given integral converges.
c.
To graph: f and g on the same screen for
c.
Answer to Problem 41E
Explanation of Solution
Given information:
Calculation:
The graph of f and g on the same screen for
From the graph
Recall that: m:math>
Since
Since 0< g(x) < f(x), so the area under g(x) is finite too.
Which in turns implies that
Chapter 5 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