CalculusVolume2-SASG-07-04
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
Chapter 7
Parametric Equations and Polar Coordinates
7.4 Area and Arc Length in Polar Coordinates
Section Exercises
For the following exercises, determine a definite integral that represents the area. 189.
Region enclosed by Answer: 191.
Region enclosed by one petal of Answer: 193.
Region below the polar axis and enclosed by Answer: 195.
Region enclosed by the inner loop of Answer: 197.
Region enclosed by and outside the inner loop
Answer: 199.
Region common to Answer: For the following exercises, find the area of the described region.
201.
Enclosed by Answer:
OpenStax Calculus Volume 2
Student Answer and Solution Guide
203.
Below the polar axis and enclosed by Answer:
OpenStax Calculus Volume 2
Student Answer and Solution Guide
205.
Enclosed by one petal of Answer: 207.
Enclosed by the inner loop of Answer: 209.
Common interior of Answer: 211.
Common interior of Answer: 213.
Common interior of Answer: For the following exercises, find a definite integral that represents the arc length.
215.
on the interval Answer: 217.
Answer: ]
For the following exercises, find the length of the curve over the given interval.
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
219.
Answer: 221.
Answer: 32
For the following exercises, use the integration capabilities of a calculator to approximate the length of the curve.
223.
[T]
Answer: 6.238
225.
[T]
Answer: 2
227.
[T]
Answer: 4.39
For the following exercises, use the familiar formula from geometry to find the area of the region described and then confirm by using the definite integral.
229.
Answer: For the following exercises, use the familiar formula from geometry to find the length of the curve and then confirm using the definite integral.
231.
Answer:
OpenStax Calculus Volume 2
Student Answer and Solution Guide
233.
Answer: For the following exercises, find the slope of a tangent line to a polar curve Let and
so the polar equation is now written in parametric form.
235.
Use the definition of the derivative and the product rule to derive the derivative of a polar equation. Answer: 237.
Answer: The slope is 239.
Answer: The slope is 0.
241.
tips of the leaves Answer: At the slope is undefined. At the slope is 0.
243.
Answer: The slope is undefined at 245.
For the cardioid find the slope of the tangent line when Answer: Slope = –1.
OpenStax Calculus Volume 2
Student Answer and Solution Guide
For the following exercises, find the slope of the tangent line to the given polar curve at the point given by the value of 247.
Answer: Slope is 249.
[T]
Use technology: at Answer: Calculator answer: –0.836.
For the following exercises, find the points at which the following polar curves have a horizontal or vertical tangent line. 251.
Answer: Horizontal tangent at 253.
The cardioid Answer: Horizontal tangents at Vertical tangents at and also at the pole This file is copyright 2016, Rice University. All Rights Reserved.
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