Concept explainers
(a)
To create a table of and values using
(a)
Explanation of Solution
Given Information:
The given parametric equations are-
Consider the parametric equations given by
(1)
The parametric equations are defined for all values ofso the domain forisSince the exponential function is always positive, bothand take on positive values only. So take few values of the parameterand find corresponding values ofandTabulate these results for better appreciation and mark each of the pointsin the coordinate plane. Join these points to get the sketch of the given parametric equations. Mark the orientation of the curve astakes on values from negative to positive. The table given below is helpful in plotting the points.
Sketch of the parametric equations is given below. The graph is extending toalong bothandaxis. Since for large values of, the exponential function with negative exponent is close to 0, one arm of the graph extends to. And for large value of, the exponential function with positive exponent tends to infinity; the other arm of the graph extends toalongaxis. The orientation of the graph is from downwards to upwards for all values of
To find out the rectangular equation by eliminating the parameterfrom the two given equations.
Explanation of Solution
Given Information:
The given parametric equations are-
Calculation:
From the first of the parametric equationsin terms ofis given by
Substitute this value ofin terms ofin the second parametric equation to get
Therefore, the equation in rectangular coordinates for the given parametric equations is-
Chapter 10 Solutions
EBK PRECALCULUS W/LIMITS
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning