 14.3.1: Explain with pictures what is meant by a simple curve and a closed ...
 14.3.2: Explain with pictures what is meant by a connected region and a sim...
 14.3.3: How do you determine whether a vector field in _2 is conservative (...
 14.3.4: How do you determine whether a vector field in _3 is conservative?
 14.3.5: Briefly describe how to find a potential function w for a conservat...
 14.3.6: If F is a conservative vector field on a region R, how do you evalu...
 14.3.7: If F is a conservative vector field on a region R, what is the valu...
 14.3.8: Give three equivalent properties of conservative vector fields.
 14.3.9: 914. Testing for conservative vector fields Determine whether the f...
 14.3.10: 914. Testing for conservative vector fields Determine whether the f...
 14.3.11: 914. Testing for conservative vector fields Determine whether the f...
 14.3.12: 914. Testing for conservative vector fields Determine whether the f...
 14.3.13: 914. Testing for conservative vector fields Determine whether the f...
 14.3.14: 914. Testing for conservative vector fields Determine whether the f...
 14.3.15: 1526. Finding potential functions Determine whether the following v...
 14.3.16: 1526. Finding potential functions Determine whether the following v...
 14.3.17: 1526. Finding potential functions Determine whether the following v...
 14.3.18: 1526. Finding potential functions Determine whether the following v...
 14.3.19: 1526. Finding potential functions Determine whether the following v...
 14.3.20: 1526. Finding potential functions Determine whether the following v...
 14.3.21: 1526. Finding potential functions Determine whether the following v...
 14.3.22: 1526. Finding potential functions Determine whether the following v...
 14.3.23: 1526. Finding potential functions Determine whether the following v...
 14.3.24: 1526. Finding potential functions Determine whether the following v...
 14.3.25: 1526. Finding potential functions Determine whether the following v...
 14.3.26: 1526. Finding potential functions Determine whether the following v...
 14.3.27: 2732. Evaluating line integrals Evaluate the line integral 1C w # d...
 14.3.28: 2732. Evaluating line integrals Evaluate the line integral 1C w # d...
 14.3.29: 2732. Evaluating line integrals Evaluate the line integral 1C w # d...
 14.3.30: 2732. Evaluating line integrals Evaluate the line integral 1C w # d...
 14.3.31: 2732. Evaluating line integrals Evaluate the line integral 1C w # d...
 14.3.32: 2732. Evaluating line integrals Evaluate the line integral 1C w # d...
 14.3.33: 3338. Line integrals of vector fields on closed curves Evaluate AC ...
 14.3.34: 3338. Line integrals of vector fields on closed curves Evaluate AC ...
 14.3.35: 3338. Line integrals of vector fields on closed curves Evaluate AC ...
 14.3.36: 3338. Line integrals of vector fields on closed curves Evaluate AC ...
 14.3.37: 3338. Line integrals of vector fields on closed curves Evaluate AC ...
 14.3.38: 3338. Line integrals of vector fields on closed curves Evaluate AC ...
 14.3.39: Explain why or why not Determine whether the following statements a...
 14.3.40: 4043. Line integrals Evaluate each line integral using a method of ...
 14.3.41: 4043. Line integrals Evaluate each line integral using a method of ...
 14.3.42: 4043. Line integrals Evaluate each line integral using a method of ...
 14.3.43: 4043. Line integrals Evaluate each line integral using a method of ...
 14.3.44: Closed curve integrals Evaluate AC ds, AC dx, and AC dy, where C is...
 14.3.45: 4548. Work in force fields Find the work required to move an object...
 14.3.46: 4548. Work in force fields Find the work required to move an object...
 14.3.47: 4548. Work in force fields Find the work required to move an object...
 14.3.48: 4548. Work in force fields Find the work required to move an object...
 14.3.49: 4950. Work from graphs Determine whether 1C F # dr along the paths ...
 14.3.50: 4950. Work from graphs Determine whether 1C F # dr along the paths ...
 14.3.51: Work by a constant force Evaluate a line integral to show that the ...
 14.3.52: Conservation of energy Suppose an object with mass m moves in a reg...
 14.3.53: Gravitational potential The gravitational force between two point m...
 14.3.54: Radial fields in _3 are conservative Prove that the radial field F ...
 14.3.55: Rotation fields are usually not conservative a. Prove that the rota...
 14.3.56: Linear and quadratic vector fields a. For what values of a, b, c, a...
 14.3.57: Alternative construction of potential functions in _2 Assume that t...
 14.3.58: 5861. Alternative construction of potential functions Use the proce...
 14.3.59: 5861. Alternative construction of potential functions Use the proce...
 14.3.60: 5861. Alternative construction of potential functions Use the proce...
 14.3.61: 5861. Alternative construction of potential functions Use the proce...
Solutions for Chapter 14.3: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 14.3
Get Full SolutionsChapter 14.3 includes 61 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 61 problems in chapter 14.3 have been answered, more than 60851 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345.

Branches
The two separate curves that make up a hyperbola

Difference of functions
(ƒ  g)(x) = ƒ(x)  g(x)

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

Empty set
A set with no elements

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

Exponential regression
A procedure for fitting an exponential function to a set of data.

Graphical model
A visible representation of a numerical or algebraic model.

Hyperboloid of revolution
A surface generated by rotating a hyperbola about its transverse axis, p. 607.

Identity function
The function ƒ(x) = x.

Integrable over [a, b] Lba
ƒ1x2 dx exists.

Open interval
An interval that does not include its endpoints.

Partial sums
See Sequence of partial sums.

Polynomial in x
An expression that can be written in the form an x n + an1x n1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

Principle of mathematical induction
A principle related to mathematical induction.

Rational expression
An expression that can be written as a ratio of two polynomials.

Recursively defined sequence
A sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms.

Regression model
An equation found by regression and which can be used to predict unknown values.

Spiral of Archimedes
The graph of the polar curve.

Synthetic division
A procedure used to divide a polynomial by a linear factor, x  a

Translation
See Horizontal translation, Vertical translation.