 14.3.1: In Exercises 14, the region for the integral is shown. State whethe...
 14.3.2: In Exercises 14, the region for the integral is shown. State whethe...
 14.3.3: In Exercises 14, the region for the integral is shown. State whethe...
 14.3.4: In Exercises 14, the region for the integral is shown. State whethe...
 14.3.5: In Exercises 58, use polar coordinates to describe the region shown.
 14.3.6: In Exercises 58, use polar coordinates to describe the region shown.
 14.3.7: In Exercises 58, use polar coordinates to describe the region shown.
 14.3.8: In Exercises 58, use polar coordinates to describe the region shown.
 14.3.9: In Exercises 914, evaluate the double integral and sketch the regio...
 14.3.10: In Exercises 914, evaluate the double integral and sketch the regio...
 14.3.11: In Exercises 914, evaluate the double integral and sketch the regio...
 14.3.12: In Exercises 914, evaluate the double integral and sketch the regio...
 14.3.13: In Exercises 914, evaluate the double integral and sketch the regio...
 14.3.14: In Exercises 914, evaluate the double integral and sketch the regio...
 14.3.15: In Exercises 1520, evaluate the iterated integral by converting to ...
 14.3.16: In Exercises 1520, evaluate the iterated integral by converting to ...
 14.3.17: In Exercises 1520, evaluate the iterated integral by converting to ...
 14.3.18: In Exercises 1520, evaluate the iterated integral by converting to ...
 14.3.19: In Exercises 1520, evaluate the iterated integral by converting to ...
 14.3.20: In Exercises 1520, evaluate the iterated integral by converting to ...
 14.3.21: In Exercises 21 and 22, combine the sum of the two iterated integra...
 14.3.22: In Exercises 21 and 22, combine the sum of the two iterated integra...
 14.3.23: In Exercises 2326, use polar coordinates to set up and evaluate the...
 14.3.24: In Exercises 2326, use polar coordinates to set up and evaluate the...
 14.3.25: In Exercises 2326, use polar coordinates to set up and evaluate the...
 14.3.26: In Exercises 2326, use polar coordinates to set up and evaluate the...
 14.3.27: Volume In Exercises 2732, use a double integral in polar coordinate...
 14.3.28: Volume In Exercises 2732, use a double integral in polar coordinate...
 14.3.29: Volume In Exercises 2732, use a double integral in polar coordinate...
 14.3.30: Volume In Exercises 2732, use a double integral in polar coordinate...
 14.3.31: Volume In Exercises 2732, use a double integral in polar coordinate...
 14.3.32: Volume In Exercises 2732, use a double integral in polar coordinate...
 14.3.33: Volume Find such that the volume inside the hemisphere and outside ...
 14.3.34: Volume Use a double integral in polar coordinates to find the volum...
 14.3.35: Volume Determine the diameter of a hole that is drilled vertically ...
 14.3.36: Machine Design The surfaces of a doublelobed cam are modeled by th...
 14.3.37: In Exercises 3742, use a double integral to find the area of the sh...
 14.3.38: In Exercises 3742, use a double integral to find the area of the sh...
 14.3.39: In Exercises 3742, use a double integral to find the area of the sh...
 14.3.40: In Exercises 3742, use a double integral to find the area of the sh...
 14.3.41: In Exercises 3742, use a double integral to find the area of the sh...
 14.3.42: In Exercises 3742, use a double integral to find the area of the sh...
 14.3.43: Describe the partition of the region of integration in the plane wh...
 14.3.44: Explain how to change from rectangular coordinates to polar coordin...
 14.3.45: In your own words, describe simple regions and simple regions.
 14.3.46: Each figure shows a region of integration for the double integral F...
 14.3.47: Think About It Consider the program you wrote to approximate double...
 14.3.48: Approximation Horizontal cross sections of a piece of ice that brok...
 14.3.49: Approximation In Exercises 49 and 50, use a computer algebra system...
 14.3.50: Approximation In Exercises 49 and 50, use a computer algebra system...
 14.3.51: Approximation In Exercises 51 and 52, determine which value best ap...
 14.3.52: Approximation In Exercises 51 and 52, determine which value best ap...
 14.3.53: True or False? In Exercises 53 and 54, determine whether the statem...
 14.3.54: True or False? In Exercises 53 and 54, determine whether the statem...
 14.3.55: Probability The value of the integral is required in the developmen...
 14.3.56: Use the result of Exercise 55 and a change of variables to evaluate...
 14.3.57: Population The population density of a city is approximated by the ...
 14.3.58: Probability Find such that the function is a probability density fu...
 14.3.59: Think About It Consider the region bounded by the graphs of and and...
 14.3.60: Repeat Exercise 59 for a region bounded by the graph of the equatio...
 14.3.61: Show that the area of the polar sector (see figure) is where is the...
Solutions for Chapter 14.3: Change of Variables: Polar Coordinates
Full solutions for Calculus: Early Transcendental Functions  4th Edition
ISBN: 9780618606245
Solutions for Chapter 14.3: Change of Variables: Polar Coordinates
Get Full SolutionsSince 61 problems in chapter 14.3: Change of Variables: Polar Coordinates have been answered, more than 45285 students have viewed full stepbystep solutions from this chapter. Chapter 14.3: Change of Variables: Polar Coordinates includes 61 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions , edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9780618606245.

Absolute value of a vector
See Magnitude of a vector.

Arithmetic sequence
A sequence {an} in which an = an1 + d for every integer n ? 2 . The number d is the common difference.

Average rate of change of ƒ over [a, b]
The number ƒ(b)  ƒ(a) b  a, provided a ? b.

Categorical variable
In statistics, a nonnumerical variable such as gender or hair color. Numerical variables like zip codes, in which the numbers have no quantitative significance, are also considered to be categorical.

Causation
A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable

Combinations of n objects taken r at a time
There are nCr = n! r!1n  r2! such combinations,

Common ratio
See Geometric sequence.

Cone
See Right circular cone.

Damping factor
The factor Aea in an equation such as y = Aeat cos bt

Difference of functions
(ƒ  g)(x) = ƒ(x)  g(x)

Directrix of a parabola, ellipse, or hyperbola
A line used to determine the conic

Domain of validity of an identity
The set of values of the variable for which both sides of the identity are defined

Horizontal asymptote
The line is a horizontal asymptote of the graph of a function ƒ if lim x: q ƒ(x) = or lim x: q ƒ(x) = b

Linear equation in x
An equation that can be written in the form ax + b = 0, where a and b are real numbers and a Z 0

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

Range screen
See Viewing window.

Sine
The function y = sin x.

Solve an equation or inequality
To find all solutions of the equation or inequality

Vertex form for a quadratic function
ƒ(x) = a(x  h)2 + k

xintercept
A point that lies on both the graph and the xaxis,.