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# Solutions for Chapter 15: Multiple Integrals

## Full solutions for Thomas' Calculus | 12th Edition

ISBN: 9780321587992

Solutions for Chapter 15: Multiple Integrals

Solutions for Chapter 15
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##### ISBN: 9780321587992

Thomas' Calculus was written by Sieva Kozinsky and is associated to the ISBN: 9780321587992. Since 54 problems in chapter 15: Multiple Integrals have been answered, more than 3962 students have viewed full step-by-step solutions from this chapter. Chapter 15: Multiple Integrals includes 54 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: Thomas' Calculus, edition: 12.

Key Calculus Terms and definitions covered in this textbook
• Additive identity for the complex numbers

0 + 0i is the complex number zero

• Angle of depression

The acute angle formed by the line of sight (downward) and the horizontal

• Annual percentage rate (APR)

The annual interest rate

• Arccosine function

See Inverse cosine function.

• Binomial probability

In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n - k2!pk11 - p) n-k where p is the probability of the outcome occurring once

• Cotangent

The function y = cot x

• Hyperboloid of revolution

A surface generated by rotating a hyperbola about its transverse axis, p. 607.

• Length of an arrow

See Magnitude of an arrow.

• Linear inequality in x

An inequality that can be written in the form ax + b < 0 ,ax + b … 0 , ax + b > 0, or ax + b Ú 0, where a and b are real numbers and a Z 0

• Logarithmic function with base b

The inverse of the exponential function y = bx, denoted by y = logb x

• Multiplicative inverse of a real number

The reciprocal of b, or 1/b, b Z 0

• Number line graph of a linear inequality

The graph of the solutions of a linear inequality (in x) on a number line

• Projection of u onto v

The vector projv u = au # vƒvƒb2v

• Row echelon form

A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

• Scalar

A real number.

• Slope

Ratio change in y/change in x

• Solution of a system in two variables

An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

• Standard form of a polynomial function

ƒ(x) = an x n + an-1x n-1 + Á + a1x + a0

• Sum of an infinite series

See Convergence of a series

• xy-plane

The points x, y, 0 in Cartesian space.

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