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# Solutions for Chapter 3.5: The Cauchy Criterion

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

ISBN: 9780471321484

Solutions for Chapter 3.5: The Cauchy Criterion

Solutions for Chapter 3.5
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##### ISBN: 9780471321484

This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. Chapter 3.5: The Cauchy Criterion includes 14 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 14 problems in chapter 3.5: The Cauchy Criterion have been answered, more than 2540 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.

Key Calculus Terms and definitions covered in this textbook
• Additive inverse of a real number

The opposite of b , or -b

• Ambiguous case

The case in which two sides and a nonincluded angle can determine two different triangles

• Angle of depression

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

• Center

The central point in a circle, ellipse, hyperbola, or sphere

• Confounding variable

A third variable that affects either of two variables being studied, making inferences about causation unreliable

• Domain of a function

The set of all input values for a function

• Frequency (in statistics)

The number of individuals or observations with a certain characteristic.

• Inequality

A statement that compares two quantities using an inequality symbol

• Inverse properties

a + 1-a2 = 0, a # 1a

• kth term of a sequence

The kth expression in the sequence

• Linear combination of vectors u and v

An expression au + bv , where a and b are real numbers

• Lower bound of f

Any number b for which b < ƒ(x) for all x in the domain of ƒ

• Magnitude of an arrow

The magnitude of PQ is the distance between P and Q

• Phase shift

See Sinusoid.

• Piecewise-defined function

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

• Real zeros

Zeros of a function that are real numbers.

• Response variable

A variable that is affected by an explanatory variable.

• Secant

The function y = sec x.

• Singular matrix

A square matrix with zero determinant

• Wrapping function

The function that associates points on the unit circle with points on the real number line

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