To explain: Geometrically of the given statement.
Answer to Problem 30E
In each interval
Explanation of Solution
Given information:
The length of small arcs when search for a Riemann sums that leads the formula for arc length.
Calculation:
Let's say wanted to calculate the lengths of small arcs using segments of horizontal lines.
Then, the sum that would roughly represent the curve's length would be
over the partition. Suppose that the partition is given over the interval
:
Take the limit and get,
The reason why this does not work is because
In each interval
Chapter 7 Solutions
CALCULUS:GRAPHICAL,...,AP ED.-W/ACCESS
- 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