Concept explainers
(a)
To find: The position of the point P in the given process and to check whether P have a limiting position.
(a)
Answer to Problem 10P
The limiting position is
Explanation of Solution
Graph:
Calculation:
Let the
From the triangle
And from the triangle
By using double-integral formula for tangents,
Simplifying above equation
Applying cross multiplication
As the altitude AM decreases in length, the point P will approach the x-axis, means y approaches to 0. So the limiting location of P exists and it must be one of the root of the equation. The point P can never be to the left of the altitude AM, so here x not equal to zero, so it must be
Thus, the limiting position is
(b)
To find: The equation of the curve and sketch the path traced out by P.
(b)
Answer to Problem 10P
The P only traces out the part of the curve with
Explanation of Solution
Graph:
Calculation:
Take the equation (1) from the part (a)
As
Thus, P only traces out the part of the curve with
Chapter 2 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