 14.1: Explain why or why not Determine whether the following statements a...
 14.2: Matching vector fields Match vector fields af with the graphs AF. L...
 14.3: 34. Gradient fields in 2 Find the vector field F = w for the f ollo...
 14.4: 34. Gradient fields in 2 Find the vector field F = w for the f ollo...
 14.5: 56. Gradient fields in 3 Find the vector field F = w for the follow...
 14.6: 56. Gradient fields in 3 Find the vector field F = w for the follow...
 14.7: Normal component Let C be the circle of radius 2 centered at the or...
 14.8: 810. Line integrals Evaluate the following line integrals. L C 1x2 ...
 14.9: 810. Line integrals Evaluate the following line integrals. L C yex...
 14.10: 810. Line integrals Evaluate the following line integrals. L C 1xz ...
 14.11: Two parameterizations Verify that AC 1x  2y + 3z2 ds has the same ...
 14.12: Work integral Find the work done in moving an object from P11, 0, 0...
 14.13: 1314. Work integrals in 3 Given the following force fields, find th...
 14.14: 1314. Work integrals in 3 Given the following force fields, find th...
 14.15: 1518. Circulation and flux Find the circulation and the outward flu...
 14.16: 1518. Circulation and flux Find the circulation and the outward flu...
 14.17: 1518. Circulation and flux Find the circulation and the outward flu...
 14.18: 1518. Circulation and flux Find the circulation and the outward flu...
 14.19: Flux in channel flow Consider the flow of water in a channel whose ...
 14.20: 2023. Conservative vector fields and potentials Determine whether t...
 14.21: 2023. Conservative vector fields and potentials Determine whether t...
 14.22: 2023. Conservative vector fields and potentials Determine whether t...
 14.23: 2023. Conservative vector fields and potentials Determine whether t...
 14.24: 2427. Evaluating line integrals Evaluate the line integral 1C F # d...
 14.25: 2427. Evaluating line integrals Evaluate the line integral 1C F # d...
 14.26: 2427. Evaluating line integrals Evaluate the line integral 1C F # d...
 14.27: 2427. Evaluating line integrals Evaluate the line integral 1C F # d...
 14.28: Radial fields in _2 are conservative Prove that the radial field F ...
 14.29: 2932. Greens Theorem for line integrals Use either form of Greens T...
 14.30: 2932. Greens Theorem for line integrals Use either form of Greens T...
 14.31: 2932. Greens Theorem for line integrals Use either form of Greens T...
 14.32: 2932. Greens Theorem for line integrals Use either form of Greens T...
 14.33: 3334. Areas of plane regions Find the area of the following regions...
 14.34: 3334. Areas of plane regions Find the area of the following regions...
 14.35: 3536. Circulation and flux Consider the following vector fields. a....
 14.36: 3536. Circulation and flux Consider the following vector fields. a....
 14.37: Parameters Let F = 8ax + by, cx + dy9, where a, b, c, and d are con...
 14.38: 3841. Divergence and curl Compute the divergence and curl of the fo...
 14.39: 3841. Divergence and curl Compute the divergence and curl of the fo...
 14.40: 3841. Divergence and curl Compute the divergence and curl of the fo...
 14.41: 3841. Divergence and curl Compute the divergence and curl of the fo...
 14.42: Identities Prove that _a 1 _ r _4 b =  4r _ r _6 and use the resul...
 14.43: Maximum curl Let F = 8z, x, y9. a. What is the component of curl F...
 14.44: Paddle wheel in a vector field Let F = 80, 2x, 09 and let n be a un...
 14.45: 4548. Surface areas Use a surface integral to find the area of the ...
 14.46: 4548. Surface areas Use a surface integral to find the area of the ...
 14.47: 4548. Surface areas Use a surface integral to find the area of the ...
 14.48: 4548. Surface areas Use a surface integral to find the area of the ...
 14.49: OS 11 + yz2 dS; S is the plane x + y + z = 2 in the first octant.
 14.50: OS 80, y, z9 # n dS; S is the curved surface of the cylinder y2 + z...
 14.51: OS 1x  y + z2 dS; S is the entire surface including the base of th...
 14.52: F = 8x, y, z9 across the curved surface of the cylinder x2 + y2 = 1...
 14.53: F = r> _ r _ across the sphere of radius a centered at the origin, ...
 14.54: Three methods Find the surface area of the paraboloid z = x2 + y2, ...
 14.55: Flux across hemispheres and paraboloids Let S be the hemisphere x2 ...
 14.56: Surface area of an ellipsoid Consider the ellipsoid x2>a2 + y2>b2 +...
 14.57: F = 8xz, yz, xy9; C is the circle x2 + y2 = 4 in the xyplane.
 14.58: F = 8x2  y2, x, 2yz9; C is the boundary of the plane z = 6  2x  ...
 14.59: F = 8 z, x, y9, where S is the hyperboloid z = 10  21 + x2 + y2, ...
 14.60: F = 8x2  z2, y2, xz9, where S is the hemisphere x2 + y2 + z2 = 4, ...
 14.61: Conservative fields Use Stokes Theorem to find the circulation of t...
 14.62: F = 8 x, x  y, x  z9; S is the surface of the cube cut from the ...
 14.63: F = 8x3, y3, z39 >3; S is the sphere 51x, y, z2: x2 + y2 + z2 = 96.
 14.64: F = 8x2, y2, z29; S is the cylinder 51x, y, z2: x2 + y2 = 4, 0 z 86.
 14.65: F = 8x3, y3, 109; D is the region between the hemispheres of radius...
 14.66: F = r _ r _3 = 8x, y, z9 1x2 + y2 + z223>2 ; D is the region betwee...
 14.67: Flux integrals Compute the outward flux of the field F = 8x2 + x si...
 14.68: Stokes Theorem on a compound surface Consider the surface S consist...
Solutions for Chapter 14: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 14
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. This expansive textbook survival guide covers the following chapters and their solutions. Since 68 problems in chapter 14 have been answered, more than 60590 students have viewed full stepbystep solutions from this chapter. Chapter 14 includes 68 full stepbystep solutions.

Addition property of inequality
If u < v , then u + w < v + w

Aphelion
The farthest point from the Sun in a planet’s orbit

Arccosecant function
See Inverse cosecant function.

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

Cosine
The function y = cos x

Damping factor
The factor Aea in an equation such as y = Aeat cos bt

Differentiable at x = a
ƒ'(a) exists

Directed line segment
See Arrow.

Elements of a matrix
See Matrix element.

Equivalent vectors
Vectors with the same magnitude and direction.

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

Independent events
Events A and B such that P(A and B) = P(A)P(B)

Interquartile range
The difference between the third quartile and the first quartile.

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

Nonsingular matrix
A square matrix with nonzero determinant

Quadratic formula
The formula x = b 2b2  4ac2a used to solve ax 2 + bx + c = 0.

Reflection across the yaxis
x, y and (x,y) are reflections of each other across the yaxis.

Regression model
An equation found by regression and which can be used to predict unknown values.

Removable discontinuity at x = a
lim x:a ƒ(x) = limx:a+ ƒ(x) but either the common limit is not equal ƒ(a) to ƒ(a) or is not defined

Upper bound test for real zeros
A test for finding an upper bound for the real zeros of a polynomial.