 14.7.1E: Explain the meaning of the integral in Stokes' Theorem.
 14.7.2E: Explain the meaning of the integral S(? × F) · n dS in Stokes' Theo...
 14.7.3E: Explain the meaning of Stokes' Theorem.
 14.7.4E: Why does a conservative vector field produce zero circulation aroun...
 14.7.5E: Verifying Stokes' Theorem Verify that the line integral and the sur...
 14.7.6E: Verifying Stokes' Theorem Verify that the line integral and the sur...
 14.7.7E: Verifying Stokes' Theorem Verify that the line integral and the sur...
 14.7.8E: Verifying Stokes' Theorem Verify that the line integral and the sur...
 14.7.9E: Verifying Stokes' Theorem Verify that the line integral and the sur...
 14.7.39E: Maximum surface integral Let S be the paraboloid z = a(1 ? x2 ? y2)...
 14.7.10E: Verifying Stokes' Theorem Verify that the line integral and the sur...
 14.7.11E: Stokes' Theorem for evaluating line integrals Evaluate the line int...
 14.7.12E: Stokes' Theorem for evaluating line integrals Evaluate the line int...
 14.7.13E: Stokes' Theorem for evaluating line integrals Evaluate the line int...
 14.7.14E: Stokes' Theorem for evaluating line integrals Evaluate the line int...
 14.7.18E: Stokes' Theorem for evaluating surface integrals Evaluate the line ...
 14.7.19E: Stokes' Theorem for evaluating surface integrals Evaluate the line ...
 14.7.20E: Stokes' Theorem for evaluating surface integrals Evaluate the line ...
 14.7.21E: Interpreting and graphing the curl For the following velocity field...
 14.7.22E: Interpreting and graphing the curl For the following velocity field...
 14.7.23E: Interpreting and graphing the curl For the following velocity field...
 14.7.24E: Interpreting and graphing the curl For the following velocity field...
 14.7.25E: Explain why or why not Determine whether the following statements a...
 14.7.40E: Area of a region in a plane Let R be a region in a plane that has a...
 14.7.26E: Conservative fields Use stokes' Theorem to find the circula tion o...
 14.7.27E: Conservative fields Use stokes' Theorem to find the circula tion o...
 14.7.28E: Conservative fields Use stokes' Theorem to find the circula tion o...
 14.7.29E: Conservative fields Use stokes' Theorem to find the circula tion o...
 14.7.30E: Tilted disks Let S be the disk enclosed by the curve C: r(t) = ?cos...
 14.7.31E: Tilted disks Let S be the disk enclosed by the curve C: r(t) = ?cos...
 14.7.32E: Tilted disks Let S be the disk enclosed by the curve C: r(t) = ?cos...
 14.7.33E: Tilted disks Let S be the disk enclosed by the curve C: r(t) = ?cos...
 14.7.34E: Tilted disks Let S be the disk enclosed by the curve C: r(t) = ?cos...
 14.7.35E: Tilted disks Let S be the disk enclosed by the curve C: r(t) = ?cos...
 14.7.36E: No integrals Let F = ?2z, z, 2y + x? and let S be the hemisphere of...
 14.7.37E: Compound surface and boundary Begin with the paraboloid z = x2+ y2,...
 14.7.38E: Ampère's Law The French physicist AndréMarie Ampère (17751836) di...
 14.7.42AE: Radial fields and zero circulation Consider the radial vector field...
 14.7.43AE: Zero curl Consider the vector field a. Show that ? × F = 0.________...
 14.7.44AE: Average circulation Let S be a small circular disk of radius R cent...
 14.7.45AE: Proof of Stokes' Theorem Confirm the following step in the proof of...
 14.7.46AE: Stokes' Theorem on closed surfaces Prove that if F satisfies the co...
 14.7.47AE: Rotated Green's Theorem Use Stokes' Theorem to write the cir culati...
 14.7.17E: Stokes' Theorem for evaluating surface integrals Evaluate the line ...
 14.7.16E: Stokes' Theorem for evaluating line integrals Evaluate the line int...
 14.7.41E: Choosing a more convenient surface The goal is to evaluate A = (? ×...
 14.7.15E: Stokes' Theorem for evaluating line integrals Evaluate the line int...
Solutions for Chapter 14.7: Calculus: Early Transcendentals 1st Edition
Full solutions for Calculus: Early Transcendentals  1st Edition
ISBN: 9780321570567
Solutions for Chapter 14.7
Get Full SolutionsCalculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since 47 problems in chapter 14.7 have been answered, more than 118706 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 14.7 includes 47 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

Absolute value of a vector
See Magnitude of a vector.

Angle
Union of two rays with a common endpoint (the vertex). The beginning ray (the initial side) can be rotated about its endpoint to obtain the final position (the terminal side)

Bounded interval
An interval that has finite length (does not extend to ? or ?)

Combinations of n objects taken r at a time
There are nCr = n! r!1n  r2! such combinations,

Component form of a vector
If a vector’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)

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

De Moivre’s theorem
(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)

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

Explicitly defined sequence
A sequence in which the kth term is given as a function of k.

Exponential decay function
Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

Imaginary part of a complex number
See Complex number.

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

Inductive step
See Mathematical induction.

Limaçon
A graph of a polar equation r = a b sin u or r = a b cos u with a > 0 b > 0

Multiplication property of equality
If u = v and w = z, then uw = vz

Quartic function
A degree 4 polynomial function.

Quotient of functions
a ƒ g b(x) = ƒ(x) g(x) , g(x) ? 0

Radian measure
The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.

Rational zeros theorem
A procedure for finding the possible rational zeros of a polynomial.

Secant
The function y = sec x.