a.
Graph the curves.
a.
Answer to Problem 34E
Use Wolfram Alpha you can type:Equations
Graph of theequations shown below:
Explanation of Solution
Given:Use Wolfram Alpha you can type: Equations
Calculation:
Use Wolfram Alpha you can type: Equations
Graph of theequations shown below:
b.
Find the length of Cornu’s spiral from the origin to the point.
b.
Answer to Problem 34E
The length of Cornu’s spiral from the origin to the point is
Explanation of Solution
Given:Cornu’s spiral
Calculation:
As
But since the upper limit of the integral is less than the lower limit that
Negates the integral. So the spiral on the left approaches point
The form of the arc length using these equations would be
So we need the derivatives.
From the Fundamental Theorem of Calculus we get:
Plug them in and simplify.
The length fromthe origin to the point with parameter value t is the same as t.
Thus, the length of Cornu’s spiral from the origin to the point is
Chapter 6 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