 15.3.1: In Exercises 14, show that the value of is the same for each parame...
 15.3.2: In Exercises 14, show that the value of is the same for each parame...
 15.3.3: In Exercises 14, show that the value of is the same for each parame...
 15.3.4: In Exercises 14, show that the value of is the same for each parame...
 15.3.5: In Exercises 510, determine whether or not the vector field is cons...
 15.3.6: In Exercises 510, determine whether or not the vector field is cons...
 15.3.7: In Exercises 510, determine whether or not the vector field is cons...
 15.3.8: In Exercises 510, determine whether or not the vector field is cons...
 15.3.9: In Exercises 510, determine whether or not the vector field is cons...
 15.3.10: In Exercises 510, determine whether or not the vector field is cons...
 15.3.11: In Exercises 1124, find the value of the line integral (Hint: If F ...
 15.3.12: In Exercises 1124, find the value of the line integral (Hint: If F ...
 15.3.13: In Exercises 1124, find the value of the line integral (Hint: If F ...
 15.3.14: In Exercises 1124, find the value of the line integral (Hint: If F ...
 15.3.15: In Exercises 1124, find the value of the line integral (Hint: If F ...
 15.3.16: In Exercises 1124, find the value of the line integral (Hint: If F ...
 15.3.17: In Exercises 1124, find the value of the line integral (Hint: If F ...
 15.3.18: In Exercises 1124, find the value of the line integral (Hint: If F ...
 15.3.19: In Exercises 1124, find the value of the line integral (Hint: If F ...
 15.3.20: In Exercises 1124, find the value of the line integral (Hint: If F ...
 15.3.21: In Exercises 1124, find the value of the line integral (Hint: If F ...
 15.3.22: In Exercises 1124, find the value of the line integral (Hint: If F ...
 15.3.23: In Exercises 1124, find the value of the line integral (Hint: If F ...
 15.3.24: In Exercises 1124, find the value of the line integral (Hint: If F ...
 15.3.25: In Exercises 2534, evaluate the line integral using the Fundamental...
 15.3.26: In Exercises 2534, evaluate the line integral using the Fundamental...
 15.3.27: In Exercises 2534, evaluate the line integral using the Fundamental...
 15.3.28: In Exercises 2534, evaluate the line integral using the Fundamental...
 15.3.29: In Exercises 2534, evaluate the line integral using the Fundamental...
 15.3.30: In Exercises 2534, evaluate the line integral using the Fundamental...
 15.3.31: In Exercises 2534, evaluate the line integral using the Fundamental...
 15.3.32: In Exercises 2534, evaluate the line integral using the Fundamental...
 15.3.33: In Exercises 2534, evaluate the line integral using the Fundamental...
 15.3.34: In Exercises 2534, evaluate the line integral using the Fundamental...
 15.3.35: Work In Exercises 35 and 36, find the work done by the force field ...
 15.3.36: Work In Exercises 35 and 36, find the work done by the force field ...
 15.3.37: Work A stone weighing 1 pound is attached to the end of a twofoot ...
 15.3.38: Work If is a constant force vector field, show that the work done i...
 15.3.39: Work To allow a means of escape for workers in a hazardous job 50 m...
 15.3.40: Work Can you find a path for the slide wire in Exercise 39 such tha...
 15.3.43: Consider the force field shown in the figure. (a) Give a verbal arg...
 15.3.44: Wind Speed and Direction The map shows the jet stream wind speed ve...
 15.3.45: In Exercises 45 and 46, consider the force field shown in the figur...
 15.3.46: In Exercises 45 and 46, consider the force field shown in the figur...
 15.3.47: True or False? In Exercises 4750, determine whether the statement i...
 15.3.48: True or False? In Exercises 4750, determine whether the statement i...
 15.3.49: True or False? In Exercises 4750, determine whether the statement i...
 15.3.50: True or False? In Exercises 4750, determine whether the statement i...
 15.3.51: A function is called harmonic if Prove that if is harmonic, then wh...
 15.3.52: Kinetic and Potential Energy The kinetic energy of an object moving...
 15.3.53: Let (a) Show that where and (b) If for find (c) If for find (d) If ...
Solutions for Chapter 15.3: Conservative Vector Fields and Independence of Path
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 15.3: Conservative Vector Fields and Independence of Path
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus, edition: 8. Calculus was written by and is associated to the ISBN: 9780618502981. Since 51 problems in chapter 15.3: Conservative Vector Fields and Independence of Path have been answered, more than 79676 students have viewed full stepbystep solutions from this chapter. Chapter 15.3: Conservative Vector Fields and Independence of Path includes 51 full stepbystep solutions.

artesian coordinate system
An association between the points in a plane and ordered pairs of real numbers; or an association between the points in threedimensional space and ordered triples of real numbers

Backtoback stemplot
A stemplot with leaves on either side used to compare two distributions.

Basic logistic function
The function ƒ(x) = 1 / 1 + ex

Constant term
See Polynomial function

Continuous at x = a
lim x:a x a ƒ(x) = ƒ(a)

Direction vector for a line
A vector in the direction of a line in threedimensional space

Fitting a line or curve to data
Finding a line or curve that comes close to passing through all the points in a scatter plot.

Horizontal translation
A shift of a graph to the left or right.

Measure of center
A measure of the typical, middle, or average value for a data set

Multiplicative inverse of a real number
The reciprocal of b, or 1/b, b Z 0

Newton’s law of cooling
T1t2 = Tm + 1T0  Tm2ekt

Order of an m x n matrix
The order of an m x n matrix is m x n.

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

Real number
Any number that can be written as a decimal.

Semimajor axis
The distance from the center to a vertex of an ellipse.

Solve a triangle
To find one or more unknown sides or angles of a triangle

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

Trichotomy property
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.

Union of two sets A and B
The set of all elements that belong to A or B or both.

Zero factor property
If ab = 0 , then either a = 0 or b = 0.