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# Solutions for Chapter 15.7: Divergence Theorem

## Full solutions for Calculus: Early Transcendental Functions | 4th Edition

ISBN: 9780618606245

Solutions for Chapter 15.7: Divergence Theorem

Solutions for Chapter 15.7
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##### ISBN: 9780618606245

Since 28 problems in chapter 15.7: Divergence Theorem have been answered, more than 42160 students have viewed full step-by-step solutions from this chapter. Chapter 15.7: Divergence Theorem includes 28 full step-by-step solutions. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9780618606245. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions , edition: 4.

Key Calculus Terms and definitions covered in this textbook
• Absolute value of a real number

Denoted by |a|, represents the number a or the positive number -a if a < 0.

P(A or B) = P(A) + P(B) - P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

• Associative properties

a + (b + c) = (a + b) + c, a(bc) = (ab)c.

• Binomial coefficients

The numbers in Pascal’s triangle: nCr = anrb = n!r!1n - r2!

• Direction angle of a vector

The angle that the vector makes with the positive x-axis

• Directrix of a parabola, ellipse, or hyperbola

A line used to determine the conic

• 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

• Implied domain

The domain of a function’s algebraic expression.

• Line of symmetry

A line over which a graph is the mirror image of itself

• Linear factorization theorem

A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1 - z1) 1x - i z 22 Á 1x - z n where the z1 are the zeros of ƒ

• Logarithm

An expression of the form logb x (see Logarithmic function)

• Mapping

A function viewed as a mapping of the elements of the domain onto the elements of the range

• Numerical model

A model determined by analyzing numbers or data in order to gain insight into a phenomenon, p. 64.

• Opens upward or downward

A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.

• Polar coordinate system

A coordinate system whose ordered pair is based on the directed distance from a central point (the pole) and the angle measured from a ray from the pole (the polar axis)

• Product of functions

(ƒg)(x) = ƒ(x)g(x)

• Reduced row echelon form

A matrix in row echelon form with every column that has a leading 1 having 0’s in all other positions.

• Resolving a vector

Finding the horizontal and vertical components of a vector.

• Solve graphically

Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically

• Vertical component

See Component form of a vector.

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