 16.1: A vector ield F, a curve C, and a point P are shown. (a) Is yC F dr...
 16.2: Evaluate the line integral
 16.3: Evaluate the line integral
 16.4: Evaluate the line integral
 16.5: Evaluate the line integral
 16.6: Evaluate the line integral
 16.7: Evaluate the line integral
 16.8: Evaluate the line integral
 16.9: Evaluate the line integral
 16.10: Find the work done by the force ield Fsx, y, zd z i 1 x j 1 y k in ...
 16.11: Show that F is a conservative vector ield. Then ind a function f su...
 16.12: Show that F is a conservative vector ield. Then ind a function f su...
 16.13: Show that F is conservative and use this fact to evaluate yC F dr a...
 16.14: Show that F is conservative and use this fact to evaluate yC F dr a...
 16.15: Verify that Greens Theorem is true for the line integral yC xy 2 dx...
 16.16: Use Greens Theorem to evaluate y C s1 1 x 3 dx 1 2xy dy where C is ...
 16.17: Use Greens Theorem to evaluate yC x 2 y dx 2 xy 2 dy, where C is th...
 16.18: Find curl F and div F if Fsx, y, zd e 2x sin y i 1 e 2y sin z j 1 e...
 16.19: Show that there is no vector ield G such that curl G 2x i 1 3yz j 2...
 16.20: If F and G are vector ields whose component functions have continuo...
 16.21: If C is any piecewisesmooth simple closed plane curve and f and t ...
 16.22: If f and t are twice differentiable functions, show that = 2 s ftd ...
 16.23: If f is a harmonic function, that is, = 2 f 0, show that the line i...
 16.24: (a) Sketch the curve C with parametric equations x cos t y sin t z ...
 16.25: Find the area of the part of the surface z x 2 1 2y that lies above...
 16.26: (a) Find an equation of the tangent plane at the point s4, 22, 1d t...
 16.27: Evaluate the surface integral.
 16.28: Evaluate the surface integral.
 16.29: Evaluate the surface integral.
 16.30: Evaluate the surface integral.
 16.31: Verify that Stokes Theorem is true for the vector ield Fsx, y, zd x...
 16.32: Use Stokes Theorem to evaluate yyS curl F dS, where Fsx, y, zd x 2 ...
 16.33: Use Stokes Theorem to evaluate yC F dr, where Fsx, y, zd xy i 1 yz ...
 16.34: Use the Divergence Theorem to calculate the surface integral yyS F ...
 16.35: Verify that the Divergence Theorem is true for the vector ield Fsx,...
 16.36: Compute the outward lux of Fsx, y, zd x i 1 y j 1 z k sx 2 1 y 2 1 ...
 16.37: Let Fsx, y, zd s3x 2 yz 2 3yd i 1 sx 3 z 2 3xd j 1 sx 3 y 1 2zd k E...
 16.38: Let Fsx, yd s2x 3 1 2xy 2 2 2yd i 1 s2y 3 1 2x 2 y 1 2xd j x 2 1 y ...
 16.39: Find yyS F n dS, where Fsx, y, zd x i 1 y j 1 z k and S is the outw...
 16.40: If the components of F have continuous second partial derivatives a...
 16.41: If a is a constant vector, r x i 1 y j 1 z k, and S is an oriented,...
Solutions for Chapter 16: Calculus: Early Transcendentals 8th Edition
Full solutions for Calculus: Early Transcendentals  8th Edition
ISBN: 9781285741550
Solutions for Chapter 16
Get Full SolutionsChapter 16 includes 41 full stepbystep solutions. Since 41 problems in chapter 16 have been answered, more than 7994 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 8. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781285741550.

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

Combinatorics
A branch of mathematics related to determining the number of elements of a set or the number of ways objects can be arranged or combined

Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)

Division
a b = aa 1 b b, b Z 0

Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2

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

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

Matrix element
Any of the real numbers in a matrix

Multiplication principle of counting
A principle used to find the number of ways an event can occur.

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

Radius
The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).

Real part of a complex number
See Complex number.

Reciprocal function
The function ƒ(x) = 1x

Reciprocal of a real number
See Multiplicative inverse of a real number.

Remainder polynomial
See Division algorithm for polynomials.

Second
Angle measure equal to 1/60 of a minute.

Seconddegree equation in two variables
Ax 2 + Bxy + Cy2 + Dx + Ey + F = 0, where A, B, and C are not all zero.

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 line test
A test for determining whether a graph is a function.

Wrapping function
The function that associates points on the unit circle with points on the real number line