 20.3.1: In Exercises 16, is the vector field a gradient field?F = 2xi + zj ...
 20.3.2: In Exercises 16, is the vector field a gradient field?F = yi + zj + xk
 20.3.3: In Exercises 16, is the vector field a gradient field?F = (y + 2z)i...
 20.3.4: In Exercises 16, is the vector field a gradient field?F = (y 2z)i +...
 20.3.5: In Exercises 16, is the vector field a gradient field?G = yi + xj
 20.3.6: In Exercises 16, is the vector field a gradient field?F = yzi + (xz...
 20.3.7: In Exercises 712, is the vector field a curl field?F = zi + xj + yk
 20.3.8: In Exercises 712, is the vector field a curl field?F = zi + yj + xk
 20.3.9: In Exercises 712, is the vector field a curl field?F = 2xi yj zk
 20.3.10: In Exercises 712, is the vector field a curl field?F = (x + y)i + (...
 20.3.11: In Exercises 712, is the vector field a curl field?F = (xy)i + (2yz...
 20.3.12: In Exercises 712, is the vector field a curl field?F = (xy)i + (xy)...
 20.3.13: In Exercises 1316, can the curl test and the divergence testbe appl...
 20.3.14: In Exercises 1316, can the curl test and the divergence testbe appl...
 20.3.15: In Exercises 1316, can the curl test and the divergence testbe appl...
 20.3.16: In Exercises 1316, can the curl test and the divergence testbe appl...
 20.3.17: Let B = bk , for some constant b. Show that the followingare all po...
 20.3.18: Find a vector field F such that curl F = 2i 3j + 4k .[Hint: Try F =...
 20.3.19: Find a vector potential for the constant vector field Bwhose value ...
 20.3.20: Express (3x + 2y)i + (4x + 9y)j as the sum of a curlfreevector fiel...
 20.3.21: In 2122, does a vector potential exist for the vectorfield given? I...
 20.3.22: In 2122, does a vector potential exist for the vectorfield given? I...
 20.3.23: An electric charge q at the origin produces an electricfield E = qr...
 20.3.24: Show that A = Ic ln(x2 + y2)k is a vector potentialforB = 2Icyi + x...
 20.3.25: Suppose c is the speed of light. A thin wire along thezaxis carryi...
 20.3.26: For constant p, consider the vector field E = rr p .(a) Find curl E...
 20.3.27: Use Stokes Theorem to show that if u(x, y) and v(x, y)are two funct...
 20.3.28: The magnetic field, B , due to a magnetic dipole withmoment satisfi...
 20.3.29: Suppose that A is a vector potential for B .(a) Show that A + grad ...
 20.3.30: In 3031, explain what is wrong with the statement.The curl of a vec...
 20.3.31: In 3031, explain what is wrong with the statement.For a certain vec...
 20.3.32: In 3233, give an example of:A vector field F that is not the curl o...
 20.3.33: In 3233, give an example of:A function f such that div grad f = 0.
 20.3.34: In 3437, is the statement true or false? Give a reasonfor your answ...
 20.3.35: In 3437, is the statement true or false? Give a reasonfor your answ...
 20.3.36: In 3437, is the statement true or false? Give a reasonfor your answ...
 20.3.37: In 3437, is the statement true or false? Give a reasonfor your answ...
 20.3.38: Let f(x, y, z) be a scalar function with continuous secondpartial d...
Solutions for Chapter 20.3: THE THREE FUNDAMENTAL THEOREMS
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 20.3: THE THREE FUNDAMENTAL THEOREMS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 20.3: THE THREE FUNDAMENTAL THEOREMS includes 38 full stepbystep solutions. Since 38 problems in chapter 20.3: THE THREE FUNDAMENTAL THEOREMS have been answered, more than 13272 students have viewed full stepbystep solutions from this chapter. Calculus: Single and Multivariable was written by Patricia and is associated to the ISBN: 9780470888612. This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6.

Base
See Exponential function, Logarithmic function, nth power of a.

Binomial probability
In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n  k2!pk11  p) nk where p is the probability of the outcome occurring once

Compounded annually
See Compounded k times per year.

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

Constraints
See Linear programming problem.

Identity function
The function ƒ(x) = x.

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

Linear regression line
The line for which the sum of the squares of the residuals is the smallest possible

Matrix element
Any of the real numbers in a matrix

Midpoint (on a number line)
For the line segment with endpoints a and b, a + b2

Negative numbers
Real numbers shown to the left of the origin on a number line.

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

Projection of u onto v
The vector projv u = au # vƒvƒb2v

Reflexive property of equality
a = a

Sample standard deviation
The standard deviation computed using only a sample of the entire population.

Sine
The function y = sin x.

Stretch of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal stretch) by the constant 1/c, or all of the ycoordinates (vertical stretch) of the points by a constant c, c, > 1.

Translation
See Horizontal translation, Vertical translation.

Vertical stretch or shrink
See Stretch, Shrink.

Xmin
The xvalue of the left side of the viewing window,.
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