 12.7.1: Describe the surfaces r = R in cylindrical coordinates and = R in s...
 12.7.2: Which statement about cylindrical coordinates is correct? (a) If = ...
 12.7.3: Which statement about spherical coordinates is correct? (a) If = 0,...
 12.7.4: The level surface = 0 in spherical coordinates, usually a cone, red...
 12.7.5: For which value of 0 is = 0 a plane? Which plane?
 12.7.6: In Exercises 510, convert from rectangular to cylindrical coordinat...
 12.7.7: In Exercises 510, convert from rectangular to cylindrical coordinat...
 12.7.8: In Exercises 510, convert from rectangular to cylindrical coordinat...
 12.7.9: In Exercises 510, convert from rectangular to cylindrical coordinat...
 12.7.10: In Exercises 510, convert from rectangular to cylindrical coordinat...
 12.7.11: In Exercises 1116, describe the set in cylindrical coordinates. 11....
 12.7.12: In Exercises 1116, describe the set in cylindrical coordinates.x2 +...
 12.7.13: In Exercises 1116, describe the set in cylindrical coordinates.y2 +...
 12.7.14: In Exercises 1116, describe the set in cylindrical coordinates.x2 +...
 12.7.15: In Exercises 1116, describe the set in cylindrical coordinates.x2 +...
 12.7.16: In Exercises 1116, describe the set in cylindrical coordinates.y2 +...
 12.7.17: In Exercises 1726, sketch the set (described in cylindrical coordin...
 12.7.18: In Exercises 1726, sketch the set (described in cylindrical coordin...
 12.7.19: In Exercises 1726, sketch the set (described in cylindrical coordin...
 12.7.20: In Exercises 1726, sketch the set (described in cylindrical coordin...
 12.7.21: In Exercises 1726, sketch the set (described in cylindrical coordin...
 12.7.22: In Exercises 1726, sketch the set (described in cylindrical coordin...
 12.7.23: In Exercises 1726, sketch the set (described in cylindrical coordin...
 12.7.24: In Exercises 1726, sketch the set (described in cylindrical coordin...
 12.7.25: In Exercises 1726, sketch the set (described in cylindrical coordin...
 12.7.26: In Exercises 1726, sketch the set (described in cylindrical coordin...
 12.7.27: In Exercises 2732, find an equation of the form r = f ( , z) in cyl...
 12.7.28: In Exercises 2732, find an equation of the form r = f ( , z) in cyl...
 12.7.29: In Exercises 2732, find an equation of the form r = f ( , z) in cyl...
 12.7.30: In Exercises 2732, find an equation of the form r = f ( , z) in cyl...
 12.7.31: In Exercises 2732, find an equation of the form r = f ( , z) in cyl...
 12.7.32: In Exercises 2732, find an equation of the form r = f ( , z) in cyl...
 12.7.33: In Exercises 3338, convert from spherical to rectangular coordinate...
 12.7.34: In Exercises 3338, convert from spherical to rectangular coordinate...
 12.7.35: In Exercises 3338, convert from spherical to rectangular coordinate...
 12.7.36: In Exercises 3338, convert from spherical to rectangular coordinate...
 12.7.37: In Exercises 3338, convert from spherical to rectangular coordinate...
 12.7.38: In Exercises 3338, convert from spherical to rectangular coordinate...
 12.7.39: In Exercises 3944, convert from rectangular to spherical coordinate...
 12.7.40: In Exercises 3944, convert from rectangular to spherical coordinate...
 12.7.41: In Exercises 3944, convert from rectangular to spherical coordinate...
 12.7.42: In Exercises 3944, convert from rectangular to spherical coordinate...
 12.7.43: In Exercises 3944, convert from rectangular to spherical coordinate...
 12.7.44: In Exercises 3944, convert from rectangular to spherical coordinate...
 12.7.45: In Exercises 45 and 46, convert from cylindrical to spherical coord...
 12.7.46: In Exercises 45 and 46, convert from cylindrical to spherical coord...
 12.7.47: In Exercises 47 and 48, convert from spherical to cylindrical coord...
 12.7.48: In Exercises 47 and 48, convert from spherical to cylindrical coord...
 12.7.49: In Exercises 4954, describe the given set in spherical coordinates....
 12.7.50: In Exercises 4954, describe the given set in spherical coordinates....
 12.7.51: In Exercises 4954, describe the given set in spherical coordinates....
 12.7.52: In Exercises 4954, describe the given set in spherical coordinates....
 12.7.53: In Exercises 4954, describe the given set in spherical coordinates....
 12.7.54: In Exercises 4954, describe the given set in spherical coordinates....
 12.7.55: In Exercises 5564, sketch the set of points (described in spherical...
 12.7.56: In Exercises 5564, sketch the set of points (described in spherical...
 12.7.57: In Exercises 5564, sketch the set of points (described in spherical...
 12.7.58: In Exercises 5564, sketch the set of points (described in spherical...
 12.7.59: In Exercises 5564, sketch the set of points (described in spherical...
 12.7.60: In Exercises 5564, sketch the set of points (described in spherical...
 12.7.61: In Exercises 5564, sketch the set of points (described in spherical...
 12.7.62: In Exercises 5564, sketch the set of points (described in spherical...
 12.7.63: In Exercises 5564, sketch the set of points (described in spherical...
 12.7.64: In Exercises 5564, sketch the set of points (described in spherical...
 12.7.65: In Exercises 6570, find an equation of the form = f ( , ) in spheri...
 12.7.66: In Exercises 6570, find an equation of the form = f ( , ) in spheri...
 12.7.67: In Exercises 6570, find an equation of the form = f ( , ) in spheri...
 12.7.68: In Exercises 6570, find an equation of the form = f ( , ) in spheri...
 12.7.69: In Exercises 6570, find an equation of the form = f ( , ) in spheri...
 12.7.70: In Exercises 6570, find an equation of the form = f ( , ) in spheri...
 12.7.71: Which of (a)(c) is the equation of the cylinder of radius R in sphe...
 12.7.72: Let P1 = (1, 3, 5) and P2 = (1, 3, 5) in rectangular coordinates. I...
 12.7.73: Find the spherical angles ( , ) for Helsinki, Finland (60.1 N, 25.0...
 12.7.74: Find the longitude and latitude for the points on the globe with an...
 12.7.75: Consider a rectangular coordinate system with its origin at the cen...
 12.7.76: Find the equation in rectangular coordinates of the quadric surface...
 12.7.77: Find an equation of the form z = f (r, ) in cylindrical coordinates...
 12.7.78: Show that = 2 cos is the equation of a sphere with its center on th...
 12.7.79: An apple modeled by taking all the points in and on a sphere of rad...
 12.7.80: Repeat using inequalities in spherical coordinates.
 12.7.81: Explain the following statement: If the equation of a surface in cy...
 12.7.82: Plot the surface = 1 cos . Then plot the trace of S in the xzplane...
 12.7.83: Find equations r = g( , z) (cylindrical) and = f ( , ) (spherical) ...
 12.7.84: In Exercises 8488, a great circle on a sphere S with center O and r...
 12.7.85: In Exercises 8488, a great circle on a sphere S with center O and r...
 12.7.86: In Exercises 8488, a great circle on a sphere S with center O and r...
 12.7.87: Show that the central angle between points P and Q on a sphere (of ...
 12.7.88: In Exercises 8488, a great circle on a sphere S with center O and r...
Solutions for Chapter 12.7: Cylindrical and Spherical Coordinates
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 12.7: Cylindrical and Spherical Coordinates
Get Full SolutionsChapter 12.7: Cylindrical and Spherical Coordinates includes 88 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. Since 88 problems in chapter 12.7: Cylindrical and Spherical Coordinates have been answered, more than 41987 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885.

Aphelion
The farthest point from the Sun in a planetâ€™s orbit

Component form of a vector
If a vectorâ€™s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x, y, and zcomponents of the vector, respectively)

Compounded k times per year
Interest compounded using the formula A = Pa1 + rkbkt where k = 1 is compounded annually, k = 4 is compounded quarterly k = 12 is compounded monthly, etc.

Directed distance
See Polar coordinates.

Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x )  x 2)2 + (y1  y2)2 + (z 1  z 2)2

End behavior asymptote of a rational function
A polynomial that the function approaches as.

Extraneous solution
Any solution of the resulting equation that is not a solution of the original equation.

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

Geometric sequence
A sequence {an}in which an = an1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

Geometric series
A series whose terms form a geometric sequence.

Horizontal line
y = b.

Independent variable
Variable representing the domain value of a function (usually x).

Inductive step
See Mathematical induction.

Measure of center
A measure of the typical, middle, or average value for a data set

Negative association
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

Octants
The eight regions of space determined by the coordinate planes.

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Range screen
See Viewing window.

Sum of complex numbers
(a + bi) + (c + di) = (a + c) + (b + d)i

Triangular number
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.