 10.2.1E: Plot the points with polar coordinates and . Give two alternative s...
 10.2.2E: Write the equations that are used to express a point with polar coo...
 10.2.3E: Write the equations that are used to express a point with Cartesian...
 10.2.4E: What is the polar equation of a circle of radius ?a? centered at th...
 10.2.5E: What is the polar equation of the vertical line x = 5?
 10.2.6E: What is the polar equation of the horizontal line y = 5?
 10.2.7E: Explain three symmetries in polar graphs and how they are detected ...
 10.2.8E: Explain the Cartesiantopolar method for graphing polar curves.
 10.2.9E: Graph the points with the following polar coordinates. Give two alt...
 10.2.10E: Graph the points with the following polar coordinates. Give two alt...
 10.2.11E: Graph the points with the following polar coordinates. Give two alt...
 10.2.12E: Graph the points with the following polar coordinates. Give two alt...
 10.2.13E: Graph the points with the following polar coordinates. Give two alt...
 10.2.14E: Points in polar coordinates Give two sets of polar coordinates for ...
 10.2.15E: Converting coordinates Express the following polar coordinates in C...
 10.2.16E: Converting coordinates Express the following polar coordinates in C...
 10.2.17E: Converting coordinates Express the following polar coordinates in C...
 10.2.18E: Converting coordinates Express the following polar coordinates in C...
 10.2.19E: Converting coordinates Express the following polar coordinates in C...
 10.2.20E: Converting coordinates Express the following polar coordinates in C...
 10.2.21E: Converting coordinates Express the following Cartesian coordinates ...
 10.2.22E: Converting coordinates Express the following Cartesian coordinates ...
 10.2.23E: Converting coordinates Express the following Cartesian coordinates ...
 10.2.24E: Converting coordinates Express the following Cartesian coordinates ...
 10.2.25E: Converting coordinates Express the following Cartesian coordinates ...
 10.2.26E: Converting coordinates Express the following Cartesian coordinates ...
 10.2.27E: Simple curves Tabulate and plot enough points to sketch a rough gra...
 10.2.28E: Simple curves Tabulate and plot enough points to sketch a rough gra...
 10.2.29E: Simple curves Tabulate and plot enough points to sketch a rough gra...
 10.2.30E: Simple curves Tabulate and plot enough points to sketch a rough gra...
 10.2.31E: Polar to Cartesian coordinates Convert the following equations to C...
 10.2.32E: Polar to Cartesian coordinates Convert the following equations to C...
 10.2.33E: Polar to Cartesian coordinates Convert the following equations to C...
 10.2.34E: Polar to Cartesian coordinates Convert the following equations to C...
 10.2.35E: Polar to Cartesian coordinates Convert the following equations to C...
 10.2.36E: Polar to Cartesian coordinates Convert the following equations to C...
 10.2.37E: Graphing polar curves Graph the following equations. Use a graphing...
 10.2.38E: Graphing polar curves Graph the following equations. Use a graphing...
 10.2.39E: Graphing polar curves Graph the following equations. Use a graphing...
 10.2.40E: Graphing polar curves Graph the following equations. Use a graphing...
 10.2.41E: Graphing polar curves Graph the following equations. Use a graphing...
 10.2.42E: Graphing polar curves Graph the following equations. Use a graphing...
 10.2.43E: Graphing polar curves Graph the following equations. Use a graphing...
 10.2.44E: Graphing polar curves Graph the following equations. Use a graphing...
 10.2.45E: Matching polar and Cartesian curves A Cartesian and a polar graph o...
 10.2.46E: Matching polar and Cartesian curves A Cartesian and a polar graph o...
 10.2.47E: Matching polar and Cartesian curves A Cartesian and a polar graph o...
 10.2.48E: Matching polar and Cartesian curves A Cartesian and a polar graph o...
 10.2.49E: Using a graphing utility Use a graphing utility to graph the follow...
 10.2.50E: Using a graphing utility Use a graphing utility to graph the follow...
 10.2.51E: Using a graphing utility Use a graphing utility to graph the follow...
 10.2.52E: Using a graphing utility Use a graphing utility to graph the follow...
 10.2.53E: Using a graphing utility Use a graphing utility to graph the follow...
 10.2.54E: Using a graphing utility Use a graphing utility to graph the follow...
 10.2.55E: Using a graphing utility Use a graphing utility to graph the follow...
 10.2.56E: Using a graphing utility Use a graphing utility to graph the follow...
 10.2.57E: Explain why or why not Determine whether the following statements a...
 10.2.58E: Sets in polar coordinates Sketch the following sets of points.{(r, ...
 10.2.59E: Sets in polar coordinates Sketch the following sets of points.{(r, ...
 10.2.60E: Sets in polar coordinates Sketch the following sets of points.{(r, ...
 10.2.61E: Sets in polar coordinates Sketch the following sets of points.{(r, ...
 10.2.62E: Sets in polar coordinates Sketch the following sets of points.{(r, ...
 10.2.63E: Sets in polar coordinates Sketch the following sets of points.{(r, ...
 10.2.64E: Sets in polar coordinates Sketch the following sets of points.{(r, ...
 10.2.65E: Sets in polar coordinates Sketch the following sets of points.{(r, ...
 10.2.66E: Circles in general Show that the polar equation describes a circle ...
 10.2.67E: Circles in general Show that the polar equation describes a circle ...
 10.2.68E: Equations of circles Use the results of Exercises 66–67 to describe...
 10.2.69E: Equations of circles Use the results of Exercise to describe and gr...
 10.2.70E: Equations of circles Use the results of Exercise to describe and gr...
 10.2.71E: Equations of circles Use the results of Exercise to describe and gr...
 10.2.72E: Equations of circles Use the results of Exercise to describe and gr...
 10.2.73E: Equations of circles Use the results of Exercise to describe and gr...
 10.2.74E: Equations of circles Find equations of the circles in the figure. D...
 10.2.75E: Vertical lines Consider the polar curve r = 2 sec ?.a. Graph the cu...
 10.2.76E: Lines in polar coordinatesa. Show that an equation of the line y = ...
 10.2.77E: Equations of lines Use the result of Exercise 76 to describe and gr...
 10.2.78E: Equations of lines Use the result of Exercise 76 to describe and gr...
 10.2.79E: Equations of lines Use the result of Exercise to describe and graph...
 10.2.80E: Equations of lines Use the result of Exercise to describe and graph...
 10.2.81E: The limaçon family The equations r = a + b cos ? and r = a + b sin ...
 10.2.82E: Limiting limaçon Consider the family of limaçons r = 1 + b cos ?. D...
 10.2.83E: The lemniscate family Equations of the form r2 = a sin 2? and r2 = ...
 10.2.84E: The lemniscate family Equations of the form r2 = a sin 2? and r2 = ...
 10.2.85E: The lemniscate family Equations of the form r2 = a sin 2? and r2 = ...
 10.2.86E: The lemniscate family Equations of the form r2 = a sin 2? and r2 = ...
 10.2.87E: The rose family Equations of the form r = a sin m? or r = a cos m?,...
 10.2.88E: The rose family Equations of the form r = a sin m? or r = a cos m?,...
 10.2.89E: The rose family Equations of the form r = a sin m? or r = a cos m?,...
 10.2.90E: The rose family Equations of the form r = a sin m? or r = a cos m?,...
 10.2.91E: Number of rose petals Show that the graph of r = a sin m? or r = a ...
 10.2.92E: Spirals Graph the following spirals. Indicate the direction in whic...
 10.2.93E: Spirals Graph the following spirals. Indicate the direction in whic...
 10.2.94E: Spirals Graph the following spirals. Indicate the direction in whic...
 10.2.95E: Intersection points Points at which the graphs of r = f(?) and r = ...
 10.2.96E: Intersection points Points at which the graphs of r = f(?) and r = ...
 10.2.97E: Intersection points Points at which the graphs of r = f(?) and r = ...
 10.2.98E: Intersection points Points at which the graphs of r = f(?) and r = ...
 10.2.99E: Enhanced butterfly curve The butterfly curve of Example 8 may be en...
 10.2.100E: Finger curves Consider the curve r = f(?) = cos (a?)  1.5, where a...
 10.2.101E: EarthMars system A simplified model assumes that the orbits of Ear...
 10.2.102E: Channel flow Water flows in a shallow semicircular channel with inn...
 10.2.103AE: Special circles Show that the equation r = a cos ? + b sin ?, where...
 10.2.104AE: Cartesian lenmiscate Find the equation in Cartesian coordinates of ...
 10.2.105AE: Subtle symmetry Without using a graphing utility, determine the sym...
 10.2.106AE: Complete curves Consider the polar curve r = cos (n?/m), where n an...
Solutions for Chapter 10.2: Calculus: Early Transcendentals 1st Edition
Full solutions for Calculus: Early Transcendentals  1st Edition
ISBN: 9780321570567
Solutions for Chapter 10.2
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 106 problems in chapter 10.2 have been answered, more than 41126 students have viewed full stepbystep solutions from this chapter. Chapter 10.2 includes 106 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Calculus: Early Transcendentals was written by Sieva Kozinsky and is associated to the ISBN: 9780321570567.

Continuous at x = a
lim x:a x a ƒ(x) = ƒ(a)

Doubleblind experiment
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment

Exponential growth function
Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .

Fitting a line or curve to data
Finding a line or curve that comes close to passing through all the points in a scatter plot.

General form (of a line)
Ax + By + C = 0, where A and B are not both zero.

Horizontal Line Test
A test for determining whether the inverse of a relation is a function.

Lefthand limit of f at x a
The limit of ƒ as x approaches a from the left.

Mathematical model
A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

Order of an m x n matrix
The order of an m x n matrix is m x n.

Orthogonal vectors
Two vectors u and v with u x v = 0.

Placebo
In an experimental study, an inactive treatment that is equivalent to the active treatment in every respect except for the factor about which an inference is to be made. Subjects in a blind experiment do not know if they have been given the active treatment or the placebo.

Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

Recursively defined sequence
A sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms.

Semimajor axis
The distance from the center to a vertex of an ellipse.

Solution of a system in two variables
An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

Standard form of a polynomial function
ƒ(x) = an x n + an1x n1 + Á + a1x + a0

Transpose of a matrix
The matrix AT obtained by interchanging the rows and columns of A.

Tree diagram
A visualization of the Multiplication Principle of Probability.

Vertex of a cone
See Right circular cone.

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.
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