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# 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

Solutions for Chapter 15.3
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##### ISBN: 9780618502981

This 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 step-by-step solutions from this chapter. Chapter 15.3: Conservative Vector Fields and Independence of Path includes 51 full step-by-step solutions.

Key Calculus Terms and definitions covered in this textbook
• artesian coordinate system

An association between the points in a plane and ordered pairs of real numbers; or an association between the points in three-dimensional space and ordered triples of real numbers

• Back-to-back stemplot

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

• Basic logistic function

The function ƒ(x) = 1 / 1 + e-x

• 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 three-dimensional 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 - Tm2e-kt

• 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.

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