 17.3.1: What is the flux of F = 1, 0, 0 through a closed surface?
 17.3.2: Justify the following statement: The flux of F = x3, y3, z3 through...
 17.3.3: Which of the following expressions are meaningful (where F is a vec...
 17.3.4: Which of the following statements is correct (where F is a continuo...
 17.3.5: How does the Divergence Theorem imply that the flux of F = x2, y ez...
 17.3.6: In Exercises 516, use the Divergence Theorem to evaluate the flux S...
 17.3.7: In Exercises 516, use the Divergence Theorem to evaluate the flux S...
 17.3.8: In Exercises 516, use the Divergence Theorem to evaluate the flux S...
 17.3.9: In Exercises 516, use the Divergence Theorem to evaluate the flux S...
 17.3.10: In Exercises 516, use the Divergence Theorem to evaluate the flux S...
 17.3.11: In Exercises 516, use the Divergence Theorem to evaluate the flux S...
 17.3.12: In Exercises 516, use the Divergence Theorem to evaluate the flux S...
 17.3.13: In Exercises 516, use the Divergence Theorem to evaluate the flux S...
 17.3.14: In Exercises 516, use the Divergence Theorem to evaluate the flux S...
 17.3.15: In Exercises 516, use the Divergence Theorem to evaluate the flux S...
 17.3.16: In Exercises 516, use the Divergence Theorem to evaluate the flux S...
 17.3.17: Calculate the flux of the vector field F = 2xyi y2j + k through the...
 17.3.18: Let S1 be the closed surface consisting of S in Figure 18 together ...
 17.3.19: Let S be the halfcylinder x2 + y2 = 1, x 0, 0 z 1.Assume that F is...
 17.3.20: Volume as a Surface Integral Let F(x, y, z) = x,y,z. Prove that if ...
 17.3.21: Use Eq. (9) to calculate the volume of the unit ball as a surface i...
 17.3.22: Verify that Eq. (9) applied to the box [0, a][0, b][0, c] yields
 17.3.23: Let W be the region in Figure 19 bounded by the cylinder x2 + y2 = ...
 17.3.24: Let I = S F dS, where F(x, y, z) = 2yz r2 , xz r2 , xy r2 (r = x2 +...
 17.3.25: The velocity field of a fluid v (in meters per second) has divergen...
 17.3.26: A hose feeds into a small screen box of volume 10 cm3 that is suspe...
 17.3.27: The electric field due to a unit electric dipole oriented in the kd...
 17.3.28: Let E be the electric field due to a long, uniformly charged rod of...
 17.3.29: Let W be the region between the sphere of radius 4 and the cube of ...
 17.3.30: Let W be the region between the sphere of radius 3 and the sphere o...
 17.3.31: Find and prove a Product Rule expressing div(f F) in terms of div(F...
 17.3.32: Prove the identity div(F G) = curl(F) G F curl(G) Then prove that t...
 17.3.33: Prove that div(f g) = 0. In Exercises 3436, denotes the Laplace ope...
 17.3.34: Prove the identity curl(curl(F)) = (div(F)) F where F denotes F1,F2...
 17.3.35: A function satisfying = 0 is called harmonic. (a) Show that = div()...
 17.3.36: Let F = rner, where n is any number,r = (x2 + y2 + z2)1/2, and er =...
 17.3.37: Let S be the boundary surface of a regionW in R3, and let Dn denote...
 17.3.38: Assume that is harmonic. Show that div() = 2 and conclude that S Dn...
 17.3.39: Let F = P,Q,R be a vector field defined on R3 such that div(F) = 0....
 17.3.40: Show that F(x, y, z) = 2y 1, 3z2, 2xy has a vector potential and fi...
 17.3.41: Show that F(x, y, z) = 2yez xy,y,yz z has a vector potential and fi...
 17.3.42: In the text, we observed that although the inversesquare radial ve...
Solutions for Chapter 17.3: Divergence Theorem
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 17.3: Divergence Theorem
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. Since 42 problems in chapter 17.3: Divergence Theorem have been answered, more than 40769 students have viewed full stepbystep solutions from this chapter. Chapter 17.3: Divergence Theorem includes 42 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3.

Bearing
Measure of the clockwise angle that the line of travel makes with due north

Complex conjugates
Complex numbers a + bi and a  bi

Exponential form
An equation written with exponents instead of logarithms.

Focal width of a parabola
The length of the chord through the focus and perpendicular to the axis.

Frequency table (in statistics)
A table showing frequencies.

Graph of an equation in x and y
The set of all points in the coordinate plane corresponding to the pairs x, y that are solutions of the equation.

Intercept
Point where a curve crosses the x, y, or zaxis in a graph.

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

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

Ordinary annuity
An annuity in which deposits are made at the same time interest is posted.

Polar coordinates
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

Radian
The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.

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

Transitive property
If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.

Tree diagram
A visualization of the Multiplication Principle of Probability.

Variance
The square of the standard deviation.

Vector
An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.

Work
The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.

xcoordinate
The directed distance from the yaxis yzplane to a point in a plane (space), or the first number in an ordered pair (triple), pp. 12, 629.

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.