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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 and is associated to the ISBN: 9780321587992. Since 54 problems in chapter 15: Multiple Integrals have been answered, more than 8632 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
• Arctangent function

See Inverse tangent function.

• Common logarithm

A logarithm with base 10.

• Complex plane

A coordinate plane used to represent the complex numbers. The x-axis of the complex plane is called the real axis and the y-axis is the imaginary axis

• De Moivre’s theorem

(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)

• Directed distance

See Polar coordinates.

• Fitting a line or curve to data

Finding a line or curve that comes close to passing through all the points in a scatter plot.

• Inequality symbol or

<,>,<,>.

• Intermediate Value Theorem

If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

• 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

• Linear programming problem

A method of solving certain problems involving maximizing or minimizing a function of two variables (called an objective function) subject to restrictions (called constraints)

• Magnitude of a real number

See Absolute value of a real number

• Measure of an angle

The number of degrees or radians in an angle

• Nappe

See Right circular cone.

• Order of magnitude (of n)

log n.

• Probability simulation

A numerical simulation of a probability experiment in which assigned numbers appear with the same probabilities as the outcomes of the experiment.

• Semiperimeter of a triangle

One-half of the sum of the lengths of the sides of a triangle.

• Sinusoidal regression

A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

• Summation notation

The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series

• Symmetric matrix

A matrix A = [aij] with the property aij = aji for all i and j

• Terminal side of an angle

See Angle.

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