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Solutions for Chapter 5.1: Continuous Functions

Full solutions for Introduction to Real Analysis | 3rd Edition

ISBN: 9780471321484

Solutions for Chapter 5.1: Continuous Functions

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 5.1: Continuous Functions includes 15 full step-by-step solutions. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. Since 15 problems in chapter 5.1: Continuous Functions have been answered, more than 8711 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
  • Addition property of equality

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

  • Angular speed

    Speed of rotation, typically measured in radians or revolutions per unit time

  • Arrow

    The notation PQ denoting the directed line segment with initial point P and terminal point Q.

  • Bearing

    Measure of the clockwise angle that the line of travel makes with due north

  • Bounded below

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

  • Convergence of a series

    A series aqk=1 ak converges to a sum S if imn: q ank=1ak = S

  • Degree of a polynomial (function)

    The largest exponent on the variable in any of the terms of the polynomial (function)

  • Endpoint of an interval

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

  • Heron’s formula

    The area of ¢ABC with semiperimeter s is given by 2s1s - a21s - b21s - c2.

  • Law of sines

    sin A a = sin B b = sin C c

  • n factorial

    For any positive integer n, n factorial is n! = n.(n - 1) . (n - 2) .... .3.2.1; zero factorial is 0! = 1

  • Polynomial function

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

  • Polynomial interpolation

    The process of fitting a polynomial of degree n to (n + 1) points.

  • Radian measure

    The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.

  • Rational numbers

    Numbers that can be written as a/b, where a and b are integers, and b ? 0.

  • Reflection across the y-axis

    x, y and (-x,y) are reflections of each other across the y-axis.

  • Riemann sum

    A sum where the interval is divided into n subintervals of equal length and is in the ith subinterval.

  • Solution set of an inequality

    The set of all solutions of an inequality

  • Tangent

    The function y = tan x

  • Xmax

    The x-value of the right side of the viewing window,.

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