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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

Solutions for Chapter 5.1
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##### ISBN: 9780471321484

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

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.

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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