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# Solutions for Chapter 9.4: Series of Functions

## Full solutions for Introduction to Real Analysis | 3rd Edition

ISBN: 9780471321484

Solutions for Chapter 9.4: Series of Functions

Solutions for Chapter 9.4
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##### ISBN: 9780471321484

This expansive textbook survival guide covers the following chapters and their solutions. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. Since 20 problems in chapter 9.4: Series of Functions have been answered, more than 3155 students have viewed full step-by-step solutions from this chapter. Chapter 9.4: Series of Functions includes 20 full step-by-step solutions. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3.

Key Calculus Terms and definitions covered in this textbook
• 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

• Constant

A letter or symbol that stands for a specific number,

• Constant function (on an interval)

ƒ(x 1) = ƒ(x 2) x for any x1 and x2 (in the interval)

• Conversion factor

A ratio equal to 1, used for unit conversion

• DMS measure

The measure of an angle in degrees, minutes, and seconds

• Double-blind experiment

A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment

• Equal complex numbers

Complex numbers whose real parts are equal and whose imaginary parts are equal.

• Exponential growth function

Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .

• Imaginary part of a complex number

See Complex number.

• Least-squares line

See Linear regression line.

• Limit

limx:aƒ1x2 = L means that ƒ(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a

• Matrix element

Any of the real numbers in a matrix

• nth power of a

The number with n factors of a , where n is the exponent and a is the base.

• Origin

The number zero on a number line, or the point where the x- and y-axes cross in the Cartesian coordinate system, or the point where the x-, y-, and z-axes cross in Cartesian three-dimensional space

• Parametrization

A set of parametric equations for a curve.

• Product of complex numbers

(a + bi)(c + di) = (ac - bd) + (ad + bc)i

• Singular matrix

A square matrix with zero determinant

• Transpose of a matrix

The matrix AT obtained by interchanging the rows and columns of A.

• Vertical translation

A shift of a graph up or down.

• y-axis

Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.

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