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# Solutions for Chapter 9.3: Tests for Nonabsolute Convergence

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

ISBN: 9780471321484

Solutions for Chapter 9.3: Tests for Nonabsolute Convergence

Solutions for Chapter 9.3
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##### ISBN: 9780471321484

Since 15 problems in chapter 9.3: Tests for Nonabsolute Convergence have been answered, more than 9715 students have viewed full step-by-step solutions from this chapter. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 9.3: Tests for Nonabsolute Convergence includes 15 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
• Absolute value of a vector

See Magnitude of a vector.

• Algebraic expression

A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

• Bounded above

A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

• Complex number

An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers

• Expanded form of a series

A series written explicitly as a sum of terms (not in summation notation).

• Exponential function

A function of the form ƒ(x) = a ? bx,where ?0, b > 0 b ?1

• First-degree equation in x , y, and z

An equation that can be written in the form.

• Limit at infinity

limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x:- q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large

• Lower bound for real zeros

A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

• Multiplication property of equality

If u = v and w = z, then uw = vz

• Polynomial function

A function in which ƒ(x)is a polynomial in x, p. 158.

• Quotient of functions

a ƒ g b(x) = ƒ(x) g(x) , g(x) ? 0

• Real part of a complex number

See Complex number.

• Scalar

A real number.

• Scientific notation

A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.

• Sum of functions

(ƒ + g)(x) = ƒ(x) + g(x)

• Terminal side of an angle

See Angle.

• Variable

A letter that represents an unspecified number.

• Variation

See Power function.

• Vertical translation

A shift of a graph up or down.

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