Concept explainers
a.
To graph: several members of the family of functions
a.
Answer to Problem 2P
Explanation of Solution
Given information: Given several members of the family of functions
Calculation:
Here’s a sketch for c =1 (green), c = 2 (orange),), c = 3 (purple) is given below.
Notice how the maximum width of the region is always equal to 2c and the height to
b.
To prove: conjecture in part (a).
b.
Answer to Problem 2P
Explanation of Solution
Given information:
Calculation:
Here’s a sketch for c =1 (green), c = 2 (orange),), c = 3 (purple) is given below.
First need to prove conjecture that the width of the region is always 2c .
The area of the region by integrating the function with respect to x between 0 and 2c.
Notice how c disappears from the equation and the region remains constant, as had first conjectured.
c.
To sketch: the curve traced out by the vertices (highest points) of the family of functions and finds what kind of curve this is.
c.
Answer to Problem 2P
Explanation of Solution
Given information:
Calculation:
Here’s a sketch for c =1 (green), c = 2 (orange),), c = 3 (purple) is given below.
Drawing a line over the vertices, notice that it converges towards zero as x increases, and its derivative, always negative, also converges to zero as x increases and also notice that the vertices are
d.
To find: an equation of the curve sketched in part (c).
d.
Answer to Problem 2P
Explanation of Solution
Given information:
Calculation:
Here’s a sketch for c =1 (green), c = 2 (orange),), c = 3 (purple) is given below.
The y -coordinating of the vertex by setting x = c in the original function. Hence, the vertex of
Chapter 5 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