 15.7.1: In Exercises 14, verify the Divergence Theorem by evaluating S F N ...
 15.7.2: In Exercises 14, verify the Divergence Theorem by evaluating S F N ...
 15.7.3: In Exercises 14, verify the Divergence Theorem by evaluating S F N ...
 15.7.4: In Exercises 14, verify the Divergence Theorem by evaluating S F N ...
 15.7.5: In Exercises 516, use the Divergence Theorem to evaluate S F N dSan...
 15.7.6: In Exercises 516, use the Divergence Theorem to evaluate S F N dSan...
 15.7.7: In Exercises 516, use the Divergence Theorem to evaluate S F N dSan...
 15.7.8: In Exercises 516, use the Divergence Theorem to evaluate S F N dSan...
 15.7.9: In Exercises 516, use the Divergence Theorem to evaluate S F N dSan...
 15.7.10: In Exercises 516, use the Divergence Theorem to evaluate S F N dSan...
 15.7.11: In Exercises 516, use the Divergence Theorem to evaluate S F N dSan...
 15.7.12: In Exercises 516, use the Divergence Theorem to evaluate S F N dSan...
 15.7.13: In Exercises 516, use the Divergence Theorem to evaluate S F N dSan...
 15.7.14: In Exercises 516, use the Divergence Theorem to evaluate S F N dSan...
 15.7.15: In Exercises 516, use the Divergence Theorem to evaluate S F N dSan...
 15.7.16: In Exercises 516, use the Divergence Theorem to evaluate S F N dSan...
 15.7.17: In Exercises 17 and 18, evaluate S curl F N dSwhere is the closed s...
 15.7.18: In Exercises 17 and 18, evaluate S curl F N dSwhere is the closed s...
 15.7.19: State the Divergence Theorem.
 15.7.20: How do you determine if a point in a vector field is a source, a si...
 15.7.21: Use the Divergence Theorem to verify that the volume of the solid b...
 15.7.22: Verify the result of Exercise 21 for the cube bounded by x 0,x a, y...
 15.7.23: Verify that S curl F N dS 0for any closed surface s
 15.7.24: For the constant vector field given by Fx, y, z a1i a2 j a3kverify ...
 15.7.25: Given the vector field Fx, y, z x i yj zk verify thatS F N dS 3Vwhe...
 15.7.26: Given the vector field Fx, y, z x i yj zk verify that F S F N dS 3F...
 15.7.27: In Exercises 27 and 28, prove the identity, assuming that and N mee...
 15.7.28: In Exercises 27 and 28, prove the identity, assuming that and N mee...
Solutions for Chapter 15.7: Divergence Theorem
Full solutions for Calculus: Early Transcendental Functions  4th Edition
ISBN: 9780618606245
Solutions for Chapter 15.7: Divergence Theorem
Get Full SolutionsSince 28 problems in chapter 15.7: Divergence Theorem have been answered, more than 42160 students have viewed full stepbystep solutions from this chapter. Chapter 15.7: Divergence Theorem includes 28 full stepbystep solutions. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9780618606245. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions , edition: 4.

Absolute value of a real number
Denoted by a, represents the number a or the positive number a if a < 0.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Associative properties
a + (b + c) = (a + b) + c, a(bc) = (ab)c.

Binomial coefficients
The numbers in Pascal’s triangle: nCr = anrb = n!r!1n  r2!

Direction angle of a vector
The angle that the vector makes with the positive xaxis

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

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

Implied domain
The domain of a function’s algebraic expression.

Line of symmetry
A line over which a graph is the mirror image of itself

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

Logarithm
An expression of the form logb x (see Logarithmic function)

Mapping
A function viewed as a mapping of the elements of the domain onto the elements of the range

Numerical model
A model determined by analyzing numbers or data in order to gain insight into a phenomenon, p. 64.

Opens upward or downward
A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.

Polar coordinate system
A coordinate system whose ordered pair is based on the directed distance from a central point (the pole) and the angle measured from a ray from the pole (the polar axis)

Product of functions
(ƒg)(x) = ƒ(x)g(x)

Reduced row echelon form
A matrix in row echelon form with every column that has a leading 1 having 0’s in all other positions.

Resolving a vector
Finding the horizontal and vertical components of a vector.

Solve graphically
Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically

Vertical component
See Component form of a vector.