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# Solutions for Chapter 12: FUNCTIONS OF SEVERAL VARIABLES

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

ISBN: 9780470888612

Solutions for Chapter 12: FUNCTIONS OF SEVERAL VARIABLES

Solutions for Chapter 12
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##### ISBN: 9780470888612

Since 48 problems in chapter 12: FUNCTIONS OF SEVERAL VARIABLES have been answered, more than 43442 students have viewed full step-by-step solutions from this chapter. Chapter 12: FUNCTIONS OF SEVERAL VARIABLES includes 48 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their 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.

Key Calculus Terms and definitions covered in this textbook
• Anchor

See Mathematical induction.

• Arc length formula

The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

• Conjugate axis of a hyperbola

The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

• Difference of complex numbers

(a + bi) - (c + di) = (a - c) + (b - d)i

• Factored form

The left side of u(v + w) = uv + uw.

• Fibonacci sequence

The sequence 1, 1, 2, 3, 5, 8, 13, . . ..

• 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

• Imaginary axis

See Complex plane.

• Inverse variation

See Power function.

• Irrational numbers

Real numbers that are not rational, p. 2.

• Modified boxplot

A boxplot with the outliers removed.

• Multiplicative identity for matrices

See Identity matrix

• Octants

The eight regions of space determined by the coordinate planes.

• Opens upward or downward

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

• Ordinary annuity

An annuity in which deposits are made at the same time interest is posted.

• Period

See Periodic function.

• Piecewise-defined function

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

• Subtraction

a - b = a + (-b)

• symmetric about the x-axis

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

• Symmetric property of equality

If a = b, then b = a

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