To show: One family of the curves are orthogonal trajectories to the other family.
Explanation of Solution
Given:
The curves
Derivative rules:
Chain rule:
Proof:
Obtain the slope of the curves
Thus the slope of the tangent to the curve
Obtain the slope of the curves
Thus, the slope of the equation
The product slope is computed as follows,
If
If
Substitute the value
The line
Therefore, the curves
Graph:
The family of the curves
From the graph, it is observed that the family of the curves
Chapter 3 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