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# Solutions for Chapter 13.3: THE DOT PRODUCT

## Full solutions for Calculus: Single and Multivariable | 6th Edition

ISBN: 9780470888612

Solutions for Chapter 13.3: THE DOT PRODUCT

Solutions for Chapter 13.3
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##### ISBN: 9780470888612

Since 85 problems in chapter 13.3: THE DOT PRODUCT have been answered, more than 43302 students have viewed full step-by-step solutions from this chapter. Chapter 13.3: THE DOT PRODUCT includes 85 full step-by-step solutions. This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612. This expansive textbook survival guide covers the following chapters and their solutions.

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

The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.

If u < v , then u + w < v + w

• Algebraic model

An equation that relates variable quantities associated with phenomena being studied

• Factor

In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .

• Factoring (a polynomial)

Writing a polynomial as a product of two or more polynomial factors.

• Matrix, m x n

A rectangular array of m rows and n columns of real numbers

• Multiplication property of equality

If u = v and w = z, then uw = vz

• Multiplicative inverse of a complex number

The reciprocal of a + bi, or 1 a + bi = a a2 + b2- ba2 + b2 i

• Nonsingular matrix

A square matrix with nonzero determinant

• Piecewise-defined function

A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

• Power rule of logarithms

logb Rc = c logb R, R 7 0.

• Pythagorean

Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

• Quartic function

A degree 4 polynomial function.

• Reciprocal of a real number

See Multiplicative inverse of a real number.

• Remainder theorem

If a polynomial f(x) is divided by x - c , the remainder is ƒ(c)

A graph in which (-x, -y) is on the the graph whenever (x, y) is; or a graph in which (-r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is

• Variable (in statistics)

A characteristic of individuals that is being identified or measured.

• Vertex of a parabola

The point of intersection of a parabola and its line of symmetry.

• yz-plane

The points (0, y, z) in Cartesian space.

• Zero of a function

A value in the domain of a function that makes the function value zero.

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