 16.3.1: The figure shows a curve and a contour map of a function whose grad...
 16.3.2: A table of values of a function with continuous gradient is given. ...
 16.3.3: Determine whether or not is a conservative vector field. If it is, ...
 16.3.4: Determine whether or not is a conservative vector field. If it is, ...
 16.3.5: Determine whether or not is a conservative vector field. If it is, ...
 16.3.6: Determine whether or not is a conservative vector field. If it is, ...
 16.3.7: Determine whether or not is a conservative vector field. If it is, ...
 16.3.8: Determine whether or not is a conservative vector field. If it is, ...
 16.3.9: Determine whether or not is a conservative vector field. If it is, ...
 16.3.10: Determine whether or not is a conservative vector field. If it is, ...
 16.3.11: The figure shows the vector field and three curves that start at (1...
 16.3.12: (a) Find a function such that and (b) use part (a) to evaluate alon...
 16.3.13: (a) Find a function such that and (b) use part (a) to evaluate alon...
 16.3.14: (a) Find a function such that and (b) use part (a) to evaluate alon...
 16.3.15: (a) Find a function such that and (b) use part (a) to evaluate alon...
 16.3.16: (a) Find a function such that and (b) use part (a) to evaluate alon...
 16.3.17: (a) Find a function such that and (b) use part (a) to evaluate alon...
 16.3.18: (a) Find a function such that and (b) use part (a) to evaluate alon...
 16.3.19: Show that the line integral is independent of path and evaluate the...
 16.3.20: Show that the line integral is independent of path and evaluate the...
 16.3.21: Find the work done by the force field in moving an object from to ....
 16.3.22: Find the work done by the force field in moving an object from to ....
 16.3.23: Is the vector field shown in the figure conservative? Explain.
 16.3.24: From a plot of guess whether it is conservative. Then determine whe...
 16.3.25: From a plot of guess whether it is conservative. Then determine whe...
 16.3.26: Let , where . Find curves and that are not closed and satisfy the e...
 16.3.27: Show that if the vector field is conservative and , , have continuo...
 16.3.28: Use Exercise 27 to show that the line integral is not independent o...
 16.3.29: Determine whether or not the given set is (a) open, (b) connected, ...
 16.3.30: Determine whether or not the given set is (a) open, (b) connected, ...
 16.3.31: Determine whether or not the given set is (a) open, (b) connected, ...
 16.3.32: Determine whether or not the given set is (a) open, (b) connected, ...
 16.3.33: Let . (a) Show that . (b) Show that is not independent of path. [Hi...
 16.3.34: (a) Suppose that is an inverse square force field, that is, for som...
Solutions for Chapter 16.3: The Fundamental Theorem for Line Integrals
Full solutions for Calculus,  5th Edition
ISBN: 9780534393397
Solutions for Chapter 16.3: The Fundamental Theorem for Line Integrals
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 16.3: The Fundamental Theorem for Line Integrals includes 34 full stepbystep solutions. Calculus, was written by and is associated to the ISBN: 9780534393397. Since 34 problems in chapter 16.3: The Fundamental Theorem for Line Integrals have been answered, more than 43749 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus,, edition: 5.

Angle of elevation
The acute angle formed by the line of sight (upward) and the horizontal

Argument of a complex number
The argument of a + bi is the direction angle of the vector {a,b}.

Blocking
A feature of some experimental designs that controls for potential differences between subject groups by applying treatments randomly within homogeneous blocks of subjects

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)

Eccentricity
A nonnegative number that specifies how offcenter the focus of a conic is

Equation
A statement of equality between two expressions.

Equivalent vectors
Vectors with the same magnitude and direction.

Expanded form of a series
A series written explicitly as a sum of terms (not in summation notation).

Halfangle identity
Identity involving a trigonometric function of u/2.

Histogram
A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.

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

Logistic growth function
A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + aekx, where a, b, c, and k are positive with b < 1. c is the limit to growth

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

Parameter
See Parametric equations.

Polar distance formula
The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22  2r1r2 cos 1?1  ?22

Quartic function
A degree 4 polynomial function.

Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt

Solve by substitution
Method for solving systems of linear equations.

Upper bound for real zeros
A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.

Vector equation for a line in space
The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.