 5.1.1: Prove the Sequential Criterion 5.1.3.
 5.1.2: Establish the Discontinuity Criterion 5.1.4.
 5.1.3: Let a < b < c. Suppose that f is continuous on [a, b), that g is co...
 5.1.4: If x e R, we define [x D to be the greatest integer n e Z such that...
 5.1.5: Let f be defined for all x e R, x :f: 2, by /(x) = (x2 + x  6)/(x ...
 5.1.6: Let A s; R and let f : A ~ R be continuous at a point c e A. Show t...
 5.1.7: Let f: R ~ R be continuous at c and let /(c) > 0. Show that there e...
 5.1.8: Let f: R ~ R be continuous on Rand letS:= {x e R: /(x) = 0} be the ...
 5.1.9: Let As; B s; R, let f: B ~Rand let g be the restriction off to A (t...
 5.1.10: Show that the absolute value function f (x) := lx I is continuous a...
 5.1.11: Let K > 0 and let f : R ~ R satisfy the condition If (x)  f (y) I ...
 5.1.12: Suppose that f: R ~ R is continuous on Rand that /(r) = 0 for every...
 5.1.13: Define g : R ~ R by g(x) := 2x for x rational, and g(x) := x + 3 fo...
 5.1.14: Let A:= (0, oo) and let k: A+ R be defined as follows. For x e A, ...
 5.1.15: Let f: (0, 1)+ R be bounded but such that lim f does not exist. Sh...
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
Get Full SolutionsIntroduction 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 stepbystep 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 stepbystep solutions from this chapter.

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

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 xvalue of the right side of the viewing window,.