To find: The any limit to the possible length of the curve.
Answer to Problem 31E
There is no limit to the length of the curve.
Explanation of Solution
Given information:
The curve is totally contained insides the square with vertices
Calculation:
The length of the curve that can be contained in a finite cube has no upper limit
So it is similar to trying to pack a thread with a thickness of
Find the length of
The graph below shows that it lies between the given box
The function as
Then evaluate the following integral
This can be seen is shown below:
Therefore, the required there is no limit to the length of the curve.
Chapter 7 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
- 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