CalculusVolume2-SASG-07-02
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
Chapter 7
Parametric Equations and Polar Coordinates 7.2 Calculus of Parametric Curves
Section Exercises
For the following exercises, each set of parametric equations represents a line. Without eliminating the parameter, find the slope of each line. 63.
Answer: 0
65.
Answer: For the following exercises, determine the slope of the tangent line, then find the equation of the tangent line at the given value of the parameter. 67.
Answer: 69.
Answer: Slope is undefined; For the following exercises, find all points on the curve that have the given slope. 71.
slope = 0.5 Answer: 73.
Answer: No points possible; undefined expression.
OpenStax Calculus Volume 2
Student Answer and Solution Guide
OpenStax Calculus Volume 2
Student Answer and Solution Guide
For the following exercises, write the equation of the tangent line in Cartesian coordinates for the given parameter t
.
75.
Answer: 77.
Answer: 79.
For where Find all values of t
at which a vertical tangent line exists. Answer: 81.
Find for Answer: 83.
For the curve find the slope and concavity of the curve at Answer: and so the curve is neither concave up nor concave down at Therefore, the graph is linear and has a constant slope but no concavity.
85.
Find the slope and concavity for the curve whose equation is at
Answer: the curve is concave down at 87.
Find all points on the curve at which horizontal and vertical tangents exist. Answer: No horizontal tangents. Vertical tangents at
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
For the following exercises, find 89.
Answer: For the following exercises, find points on the curve at which tangent line is horizontal or vertical. 91.
Answer: Horizontal vertical For the following exercises, find at the value of the parameter. 93.
Answer: 1
95.
Answer: 0
For the following exercises, find at the given point without eliminating the parameter. 97.
Answer: 4
99.
Determine the concavity of the curve Answer: Concave up on 101.
Find the area bounded by the curve and the lines and
Answer:
OpenStax Calculus Volume 2
Student Answer and Solution Guide
103.
Find the area of the region bounded by for Answer: For the following exercises, find the area of the regions bounded by the parametric curves and the indicated values of the parameter. 105.
[T]
Answer: 107.
[T]
(the “teardrop”) Answer: For the following exercises, find the arc length of the curve on the indicated interval of the parameter.
109.
Answer: 111.
Answer: 113.
on the interval (the hypocycloid)
Answer: 115.
Find the distance traveled by a particle with position as t
varies in the given time interval:
Answer: 117.
Show that the total length of the ellipse is
where and
OpenStax Calculus Volume 2
Student Answer and Solution Guide
For the following exercises, find the area of the surface obtained by rotating the given curve about the x
-axis.
119.
Answer: 121.
[T]
Use a CAS to find the area of the surface generated by rotating
about the x
-axis. (Answer to three decimal places.) Answer: 59.101
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
123.
Find the area of the surface generated by revolving about the x
-
axis. Answer: This file is copyright 2016, Rice University. All Rights Reserved.