 13.5.1: Explain how cylindrical coordinates are used to describe a point in...
 13.5.2: Explain how spherical coordinates are used to describe a point in _3.
 13.5.3: Describe the set 51r, u, z2: r = 4z6 in cylindrical coordinates.
 13.5.4: Describe the set 51r, w, u2: w = p>46 in spherical coordinates.
 13.5.5: Explain why dz r dr du is the volume of a small box in cylindrical ...
 13.5.6: Explain why r2 sin w dr dw du is the volume of a small box in spher...
 13.5.7: Write the integral 7D f 1r, u, z2 dV as an iterated integral where ...
 13.5.8: Write the integral 7D f 1r, w, u2 dV as an iterated integral, where...
 13.5.9: What coordinate system is suggested if the integrand of a triple in...
 13.5.10: What coordinate system is suggested if the integrand of a triple in...
 13.5.11: 1114. Sets in cylindrical coordinates Identify and sketch the follo...
 13.5.12: 1114. Sets in cylindrical coordinates Identify and sketch the follo...
 13.5.13: 1114. Sets in cylindrical coordinates Identify and sketch the follo...
 13.5.14: 1114. Sets in cylindrical coordinates Identify and sketch the follo...
 13.5.15: 1518. Integrals in cylindrical coordinates Evaluate the following i...
 13.5.16: 1518. Integrals in cylindrical coordinates Evaluate the following i...
 13.5.17: 1518. Integrals in cylindrical coordinates Evaluate the following i...
 13.5.18: 1518. Integrals in cylindrical coordinates Evaluate the following i...
 13.5.19: 1922. Integrals in cylindrical coordinates Evaluate the following i...
 13.5.20: 1922. Integrals in cylindrical coordinates Evaluate the following i...
 13.5.21: 1922. Integrals in cylindrical coordinates Evaluate the following i...
 13.5.22: 1922. Integrals in cylindrical coordinates Evaluate the following i...
 13.5.23: 2326. Mass from density Find the mass of the following objects with...
 13.5.24: 2326. Mass from density Find the mass of the following objects with...
 13.5.25: 2326. Mass from density Find the mass of the following objects with...
 13.5.26: 2326. Mass from density Find the mass of the following objects with...
 13.5.27: Which weighs more? For 0 r 1, the solid bounded by the cone z = 4 ...
 13.5.28: Which weighs more? Which of the objects in Exercise 27 weighs more ...
 13.5.29: 2934. Volumes in cylindrical coordinates Use cylindrical coordinate...
 13.5.30: 2934. Volumes in cylindrical coordinates Use cylindrical coordinate...
 13.5.31: 2934. Volumes in cylindrical coordinates Use cylindrical coordinate...
 13.5.32: 2934. Volumes in cylindrical coordinates Use cylindrical coordinate...
 13.5.33: 2934. Volumes in cylindrical coordinates Use cylindrical coordinate...
 13.5.34: 2934. Volumes in cylindrical coordinates Use cylindrical coordinate...
 13.5.35: 3538. Sets in spherical coordinates Identify and sketch the followi...
 13.5.36: 3538. Sets in spherical coordinates Identify and sketch the followi...
 13.5.37: 3538. Sets in spherical coordinates Identify and sketch the followi...
 13.5.38: 3538. Sets in spherical coordinates Identify and sketch the followi...
 13.5.39: 3945. Integrals in spherical coordinates Evaluate the following int...
 13.5.40: 3945. Integrals in spherical coordinates Evaluate the following int...
 13.5.41: 3945. Integrals in spherical coordinates Evaluate the following int...
 13.5.42: 3945. Integrals in spherical coordinates Evaluate the following int...
 13.5.43: 3945. Integrals in spherical coordinates Evaluate the following int...
 13.5.44: 3945. Integrals in spherical coordinates Evaluate the following int...
 13.5.45: 3945. Integrals in spherical coordinates Evaluate the following int...
 13.5.46: 4652. Volumes in spherical coordinates Use spherical coordinates to...
 13.5.47: 4652. Volumes in spherical coordinates Use spherical coordinates to...
 13.5.48: 4652. Volumes in spherical coordinates Use spherical coordinates to...
 13.5.49: 4652. Volumes in spherical coordinates Use spherical coordinates to...
 13.5.50: 4652. Volumes in spherical coordinates Use spherical coordinates to...
 13.5.51: 4652. Volumes in spherical coordinates Use spherical coordinates to...
 13.5.52: 4652. Volumes in spherical coordinates Use spherical coordinates to...
 13.5.53: Explain why or why not Determine whether the following statements a...
 13.5.54: Spherical to rectangular Convert the equation r2 = sec 2w, where 0 ...
 13.5.55: Spherical to rectangular Convert the equation r2 = sec 2w, where p...
 13.5.56: The ball of radius 4 centered at the origin with a density f 1r, w,...
 13.5.57: The ball of radius 8 centered at the origin with a density f 1r, w,...
 13.5.58: The solid cone 51r, u, z2: 0 z 4, 0 r 13z, 0 u 2p6 with a density f...
 13.5.59: The solid cylinder 51r, u, z2: 0 r 2, 0 u 2p, 1 z 16 with a densit...
 13.5.60: The solid outside the cylinder r = 1 and inside the sphere r = 5, f...
 13.5.61: The solid above the cone z = r and below the sphere r = 2, for z 0,...
 13.5.62: L 2p 0 L p>4 0 L 4 sec w 0 f 1r, w, u2 r2 sin w dr dw du in the ord...
 13.5.63: L 2p 0 L p>2 p>6 L 2 csc w f 1r, w, u2 r2 sin w dr dw du in the ord...
 13.5.64: The solid inside the sphere r = 1 and below the cone w = p>4, for z 0
 13.5.65: That part of the solid cylinder r 2 that lies between the cones w =...
 13.5.66: That part of the ball r 2 that lies between the cones w = p>3 and w...
 13.5.67: The solid bounded by the cylinder r = 1, for 0 z x + y
 13.5.68: The solid inside the cylinder r = 2 cos u, for 0 z 4  x
 13.5.69: The wedge cut from the cardioid cylinder r = 1 + cos u by the plane...
 13.5.70: Volume of a drilled hemisphere Find the volume of material remainin...
 13.5.71: Two cylinders The x and yaxes form the axes of two right circular...
 13.5.72: Three cylinders The coordinate axes form the axes of three right ci...
 13.5.73: Density distribution A right circular cylinder with height 8 cm and...
 13.5.74: Charge distribution A spherical cloud of electric charge has a know...
 13.5.75: Gravitational field due to spherical shell A point mass m is a dist...
 13.5.76: Water in a gas tank Before a gasolinepowered engine is started, wa...
 13.5.77: Cone Find the volume of a solid right circular cone with height h a...
 13.5.78: Spherical cap Find the volume of the cap of a sphere of radius R wi...
 13.5.79: Frustum of a cone Find the volume of a truncated solid cone of heig...
 13.5.80: Ellipsoid Find the volume of a solid ellipsoid with axes of length ...
 13.5.81: Intersecting spheres One sphere is centered at the origin and has a...
Solutions for Chapter 13.5: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 13.5
Get Full SolutionsSince 81 problems in chapter 13.5 have been answered, more than 61333 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 13.5 includes 81 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345.

Central angle
An angle whose vertex is the center of a circle

Confounding variable
A third variable that affects either of two variables being studied, making inferences about causation unreliable

Conversion factor
A ratio equal to 1, used for unit conversion

Cycloid
The graph of the parametric equations

Equal matrices
Matrices that have the same order and equal corresponding elements.

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

n factorial
For any positive integer n, n factorial is n! = n.(n  1) . (n  2) .... .3.2.1; zero factorial is 0! = 1

Objective function
See Linear programming problem.

Parabola
The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

Paraboloid of revolution
A surface generated by rotating a parabola about its line of symmetry.

PH
The measure of acidity

Principle of mathematical induction
A principle related to mathematical induction.

Projection of u onto v
The vector projv u = au # vƒvƒb2v

Real zeros
Zeros of a function that are real numbers.

Residual
The difference y1  (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.

Time plot
A line graph in which time is measured on the horizontal axis.

Tree diagram
A visualization of the Multiplication Principle of Probability.

Trichotomy property
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.

Vertical line
x = a.

Wrapping function
The function that associates points on the unit circle with points on the real number line