 16.10.1: What is a vector field? Give three examples that have physical meaning
 16.10.2: (a) What is a conservative vector field? (b) What is a potential fu...
 16.10.3: (a) Write the definition of the line integral of a scalar function ...
 16.10.4: (a) Define the line integral of a vector field along a smooth curve...
 16.10.5: State the Fundamental Theorem for Line Integrals.
 16.10.6: (a) What does it mean to say that is independent of path? (b) If yo...
 16.10.7: State Greens Theorem
 16.10.8: Write expressions for the area enclosed by a curve in terms of line...
 16.10.9: Suppose is a vector field on . (a) Define curl . (b) Define div .(c...
 16.10.10: If , how do you test to determine whether is conservative? What if ...
 16.10.11: . (a) What is a parametric surface? What are its grid curves? (b) W...
 16.10.12: (a) Write the definition of the surface integral of a scalar functi...
 16.10.13: (a) What is an oriented surface? Give an example of a nonorientable...
 16.10.14: State Stokes Theorem.
 16.10.15: State the Divergence Theorem.
 16.10.16: In what ways are the Fundamental Theorem for Line Integrals, Greens...
 16.10.17: Use Greens Theorem to evaluate , where is the circle with countercl...
 16.10.18: Find curl and div if Fx, y, z ex sin y i ey sin z j ez sin x kGcurl
 16.10.19: Show that there is no vector field such that curl G 2x i 3yz j xz2 ...
 16.10.20: Show that, under conditions to be stated on the vector fields and ,...
 16.10.21: If is any piecewisesmooth simple closed plane curve and and are di...
 16.10.22: If and are twice differentiable functions, show that 2 ft f 2t t2f ...
 16.10.23: If is a harmonic function, that is, , show that the line integral i...
 16.10.24: (a) Sketch the curve with parametric equations (b) Find .
 16.10.25: Find the area of the part of the surface that lies above the triang...
 16.10.26: (a) Find an equation of the tangent plane at the point to the param...
 16.10.27: 2730 Evaluate the surface integral.where is the part of the parabol...
 16.10.28: 2730 Evaluate the surface integral.xx S S x 2z y 2z dSx where is th...
 16.10.29: 2730 Evaluate the surface integral.xx Fx, y, z x z i 2y j 3x k S S ...
 16.10.30: 2730 Evaluate the surface integral.. , where and is thepart of the ...
 16.10.31: Verify that Stokes Theorem is true for the vector field , where is ...
 16.10.32: Use Stokes Theorem to evaluate , where , is the part of the sphere ...
 16.10.33: Use Stokes Theorem to evaluate , where , and is the triangle with v...
 16.10.34: Use the Divergence Theorem to calculate the surface integral , wher...
 16.10.35: Verify that the Divergence Theorem is true for the vector field , w...
 16.10.36: Compute the outward flux of Fx, y, z x i y j z kx 2 y 2 z2 324x 2 t...
 16.10.37: Let Evaluate , where is the curve with initial point and terminal p...
 16.10.38: Let Evaluate , where is shown in the figure.
 16.10.39: Find , where and is the outwardly oriented surface shown in the fig...
 16.10.40: If the components of have continuous second partial derivatives and...
 16.10.41: If is a constant vector, , and is an oriented, smooth surface with ...
Solutions for Chapter 16.10: Summary
Full solutions for Calculus: Early Transcendentals  7th Edition
ISBN: 9780538497909
Solutions for Chapter 16.10: Summary
Get Full SolutionsSince 41 problems in chapter 16.10: Summary have been answered, more than 31228 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 7. Chapter 16.10: Summary includes 41 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780538497909. This expansive textbook survival guide covers the following chapters and their solutions.

Cosecant
The function y = csc x

Fundamental
Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).

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

Horizontal line
y = b.

Index of summation
See Summation notation.

Linear combination of vectors u and v
An expression au + bv , where a and b are real numbers

Magnitude of an arrow
The magnitude of PQ is the distance between P and Q

Measure of an angle
The number of degrees or radians in an angle

Midpoint (in Cartesian space)
For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b

Natural numbers
The numbers 1, 2, 3, . . . ,.

Onetoone function
A function in which each element of the range corresponds to exactly one element in the domain

Origin
The number zero on a number line, or the point where the x and yaxes cross in the Cartesian coordinate system, or the point where the x, y, and zaxes cross in Cartesian threedimensional space

Projectile motion
The movement of an object that is subject only to the force of gravity

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

Rational function
Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.

Secant line of ƒ
A line joining two points of the graph of ƒ.

Sphere
A set of points in Cartesian space equally distant from a fixed point called the center.

Translation
See Horizontal translation, Vertical translation.

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

zcoordinate
The directed distance from the xyplane to a point in space, or the third number in an ordered triple.