(a.)
The graphs of the given parametric equations in the parametric interval
(a.)
![Check Mark](/static/check-mark.png)
Answer to Problem 44E
The graphs of the given parametric equations in the parametric interval
Explanation of Solution
Given:
The parametric equations;
Concept used:
The parametric equations are graphed for each of the given values of
Calculation:
The given parametric equations are
The graphs of these parametric equations in the parametric interval
When
When
When
When
It can be seen that
Conclusion:
The graphs of the given parametric equations in the parametric interval
(b.)
The graphs of the given parametric equations in the parametric interval
(b.)
![Check Mark](/static/check-mark.png)
Answer to Problem 44E
The graphs of the given parametric equations in the parametric interval
Explanation of Solution
Given:
The parametric equations;
Concept used:
The parametric equations are graphed for each of the given values of
Calculation:
The given parametric equations are
The graphs of these parametric equations in the parametric interval
When
When
When
When
It can be seen that
Conclusion:
The graphs of the given parametric equations in the parametric interval
(c.)
A parametrization of the given circle.
(c.)
![Check Mark](/static/check-mark.png)
Answer to Problem 44E
It has been determined that the parametrization of the given circle is
Explanation of Solution
Given:
The circle with radius
Concept used:
The parametrization;
Calculation:
As seen in the previous parts, the parametrization;
The given circle has radius
Then, here
The center of the given circle is at
Then, here
Put these values in
So, the parametrization of the given circle is
Conclusion:
It has been determined that the parametrization of the given circle is
(d.)
A parameterization for the given ellipse.
(d.)
![Check Mark](/static/check-mark.png)
Answer to Problem 44E
It has been determined that the parameterization for the given ellipse is
Explanation of Solution
Given:
An ellipse centered at
Concept used:
The parametrization of an ellipse centered at
Calculation:
The given ellipse is centered at
Then, here
The length of the semi-major axis of the given ellipse, parallel to the
Then, here
The length of the semi-minor axis of the given ellipse, parallel to the
Then, here
Put these values in
So, the required parametrization is
Conclusion:
It has been determined that the parameterization for the given ellipse is
Chapter 0 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
- 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
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