Solutions for Chapter 4.1: Limits of Functions

Full solutions for Introduction to Real Analysis | 3rd Edition

ISBN: 9780471321484

Solutions for Chapter 4.1: Limits of Functions

This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 4.1: Limits of Functions includes 16 full step-by-step solutions. Since 16 problems in chapter 4.1: Limits of Functions have been answered, more than 2632 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
  • Addition property of equality

    If u = v and w = z , then u + w = v + z

  • Causation

    A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable

  • Difference of complex numbers

    (a + bi) - (c + di) = (a - c) + (b - d)i

  • Direct variation

    See Power function.

  • Direction of an arrow

    The angle the arrow makes with the positive x-axis

  • Endpoint of an interval

    A real number that represents one “end” of an interval.

  • Fundamental

    Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).

  • Identity

    An equation that is always true throughout its domain.

  • Instantaneous rate of change

    See Derivative at x = a.

  • Instantaneous velocity

    The instantaneous rate of change of a position function with respect to time, p. 737.

  • Length of a vector

    See Magnitude of a vector.

  • Mode of a data set

    The category or number that occurs most frequently in the set.

  • Natural logarithm

    A logarithm with base e.

  • Odd function

    A function whose graph is symmetric about the origin (ƒ(-x) = -ƒ(x) for all x in the domain of f).

  • Outliers

    Data items more than 1.5 times the IQR below the first quartile or above the third quartile.

  • Product of a scalar and a vector

    The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

  • Right angle

    A 90° angle.

  • Standard form: equation of a circle

    (x - h)2 + (y - k2) = r 2

  • Triangular number

    A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

  • Ymin

    The y-value of the bottom of the viewing window.

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