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

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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