(a.)
The graphs of the given parametric equations in the parametric interval
(a.)
Answer to Problem 43E
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 graph of these parametric equations in the parametric interval
are as follows:
It can be seen that
Conclusion:
The graphs of the given parametric equations in the parametric interval
(b.)
The graph of the given parametric equations in the parametric interval
(b.)
Answer to Problem 43E
The graph of the given parametric equations in the parametric interval
Explanation of Solution
Given:
The parametric equations;
Concept used:
The parametric equations are graphed for the given values of
Calculation:
The given parametric equations are
Put
The graph of these parametric equations in the parametric interval
are as follows:
Conclusion:
The graph of the given parametric equations in the parametric interval
(c.)
The graph of the given parametric equations in the parametric interval
(c.)
Answer to Problem 43E
The graph of the given parametric equations in the parametric interval
An explanation for the appearance of the lines based on the parameter
Explanation of Solution
Given:
The parametric equations;
Concept used:
The parametric equations are graphed for the given values of
Calculation:
The given parametric equations are
Put
The graph of these parametric equations in the parametric interval
are as follows:
Note that both
So, both
Hence, the graph of these parametric equations is discontinuous at these points.
Since the graph is in connected mode, the dotted lines show up on the graph at these discontinuities.
Conclusion:
The graph of the given parametric equations in the parametric interval
An explanation for the appearance of the lines based on the parameter
(d.)
To Explain:
(d.)
Answer to Problem 43E
It has been explained using algebra why
Explanation of Solution
Given:
The parametric equations;
Concept used:
According to
Calculation:
The given parametric equations are;
Put these values in
Simplifying,
On further simplification,
Put
Simplifying,
This is the required expression.
Conclusion:
It has been explained using algebra why
(e.)
To Repeat: The solutions of part (a), (b) and (d) using an appropriate version of (d) for the given parametric equations.
(e.)
Answer to Problem 43E
The solutions for part (a), (b) and (d) using an appropriate version of (d) have been repeated for the given parametric equations.
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 graph of these parametric equations in the parametric interval
are as follows:
It can be seen that
The graph of the given parametric equations in the parametric interval
Now, for the given parametric equations, it follows that
This can be shown as follows:
Put the given equations;
Simplifying,
On further simplification,
Put
Simplifying,
This is the required proof.
Conclusion:
The solutions for part (a), (b) and (d) using an appropriate version of (d) have been repeated for the given parametric equations.
Chapter 0 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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