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# Solutions for Chapter 13: Functions of Several Variables

## Full solutions for Calculus | 8th Edition

ISBN: 9780618502981

Solutions for Chapter 13: Functions of Several Variables

Solutions for Chapter 13
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##### ISBN: 9780618502981

Chapter 13: Functions of Several Variables includes 100 full step-by-step solutions. This textbook survival guide was created for the textbook: Calculus, edition: 8. Since 100 problems in chapter 13: Functions of Several Variables have been answered, more than 76571 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Calculus was written by and is associated to the ISBN: 9780618502981.

Key Calculus Terms and definitions covered in this textbook
• Average rate of change of ƒ over [a, b]

The number ƒ(b) - ƒ(a) b - a, provided a ? b.

• Bounded

A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

• Completing the square

A method of adding a constant to an expression in order to form a perfect square

• Component form of a vector

If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x-, y-, and z-components of the vector, respectively)

• Difference of functions

(ƒ - g)(x) = ƒ(x) - g(x)

• Endpoint of an interval

A real number that represents one “end” of an interval.

• Graph of a function ƒ

The set of all points in the coordinate plane corresponding to the pairs (x, ƒ(x)) for x in the domain of ƒ.

• Instantaneous rate of change

See Derivative at x = a.

• Inverse sine function

The function y = sin-1 x

See Polynomial function in x

• Linear inequality in two variables x and y

An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0

• Ordered pair

A pair of real numbers (x, y), p. 12.

• PH

The measure of acidity

• Rigid transformation

A transformation that leaves the basic shape of a graph unchanged.

• Semimajor axis

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

• Sphere

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

• Sum of two vectors

<u1, u2> + <v1, v2> = <u1 + v1, u2 + v2> <u1 + v1, u2 + v2, u3 + v3>

• Term of a polynomial (function)

An expression of the form anxn in a polynomial (function).

• Tree diagram

A visualization of the Multiplication Principle of Probability.

• z-coordinate

The directed distance from the xy-plane to a point in space, or the third number in an ordered triple.

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