 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: The Divergence and Integral Tests
Full solutions for Calculus: Early Transcendentals  1st Edition
ISBN: 9780321570567
Solutions for Chapter 10.2: The Divergence and Integral Tests
Get Full SolutionsSummary of Chapter 10.2: The Divergence and Integral Tests
With geometric series and telescoping series, the sequence of partial sums can be found and its limit can be evaluated (when it exists).
This expansive textbook survival guide covers the following chapters and their solutions. Since 106 problems in chapter 10.2: The Divergence and Integral Tests have been answered, more than 407276 students have viewed full stepbystep solutions from this chapter. Chapter 10.2: The Divergence and Integral Tests 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 and is associated to the ISBN: 9780321570567.

Acute triangle
A triangle in which all angles measure less than 90°

Angle between vectors
The angle formed by two nonzero vectors sharing a common initial point

Angle of elevation
The acute angle formed by the line of sight (upward) and the horizontal

Directed angle
See Polar coordinates.

equation of a parabola
(x  h)2 = 4p(y  k) or (y  k)2 = 4p(x  h)

Identity properties
a + 0 = a, a ? 1 = a

Infinite discontinuity at x = a
limx:a + x a ƒ(x) = q6 or limx:a  ƒ(x) = q.

Inverse cotangent function
The function y = cot1 x

Irrational numbers
Real numbers that are not rational, p. 2.

Magnitude of an arrow
The magnitude of PQ is the distance between P and Q

Matrix, m x n
A rectangular array of m rows and n columns of real numbers

Nonsingular matrix
A square matrix with nonzero determinant

Quotient identities
tan ?= sin ?cos ?and cot ?= cos ? sin ?

Semiminor axis
The distance from the center of an ellipse to a point on the ellipse along a line perpendicular to the major axis.

Sequence of partial sums
The sequence {Sn} , where Sn is the nth partial sum of the series, that is, the sum of the first n terms of the series.

Stem
The initial digit or digits of a number in a stemplot.

Tangent
The function y = tan x

Transformation
A function that maps real numbers to real numbers.

xzplane
The points x, 0, z in Cartesian space.

zaxis
Usually the third dimension in Cartesian space.