 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 33263 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.

Basic logistic function
The function ƒ(x) = 1 / 1 + ex

Common ratio
See Geometric sequence.

Convergence of a sequence
A sequence {an} converges to a if limn: q an = a

Course
See Bearing.

Dependent event
An event whose probability depends on another event already occurring

DMS measure
The measure of an angle in degrees, minutes, and seconds

Fundamental
Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).

Grapher or graphing utility
Graphing calculator or a computer with graphing software.

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

Inverse of a matrix
The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.

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

Linear factorization theorem
A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1  z1) 1x  i z 22 Á 1x  z n where the z1 are the zeros of ƒ

Local extremum
A local maximum or a local minimum

Measure of spread
A measure that tells how widely distributed data are.

Newton’s law of cooling
T1t2 = Tm + 1T0  Tm2ekt

Parameter interval
See Parametric equations.

Parametric equations
Equations of the form x = ƒ(t) and y = g(t) for all t in an interval I. The variable t is the parameter and I is the parameter interval.

Perihelion
The closest point to the Sun in a planet’s orbit.

Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)

System
A set of equations or inequalities.