 5.2.1: Determine the points of continuity of the following functions and s...
 5.2.2: Show that iff : A + 1R is continuous on A ~ 1R and if n e N, then ...
 5.2.3: Give an example of functions f and g that are both discontinuous at...
 5.2.4: Let x ~ [xD denote the greatest integer function (see Exercise 5.1....
 5.2.5: Let g be defined on JR by g(l) := 0, and g(x) := 2 if x :1: 1, and ...
 5.2.6: Let f, g be defined on JR and let c e JR. Suppose that lim f = b an...
 5.2.7: Give an example of a function f : [0, 1] + JR that is discontinuou...
 5.2.8: Let f, g be continuous from JR to JR, and suppose that /(r) = g(r) ...
 5.2.9: Let h: JR+ JR be continuous on JR satisfying h(m/2") = 0 for all m...
 5.2.10: Let f: JR+ JR be continuous on JR, and let P := {x e R: /(x) > 0}....
 5.2.11: Iff and g are continuous on JR. letS := {x e R: /(x) ~ g(x)}. If (s...
 5.2.12: A function f : R + JR is said to be additive if f (x + y) = f (x) ...
 5.2.13: Suppose that f is a continuous additive function on R. If c := f (1...
 5.2.14: Let g: R+ R satisfy the relation g(x + y) = g(x)g(y) for all x, y ...
 5.2.15: Let f, g : JR+ JR be continuous at a point c, and let h(x) :=sup {...
Solutions for Chapter 5.2: Combinations of Continuous Functions
Full solutions for Introduction to Real Analysis  3rd Edition
ISBN: 9780471321484
Solutions for Chapter 5.2: Combinations of Continuous Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 15 problems in chapter 5.2: Combinations of Continuous Functions have been answered, more than 8093 students have viewed full stepbystep solutions from this chapter. Chapter 5.2: Combinations of Continuous Functions includes 15 full stepbystep solutions. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

artesian coordinate system
An association between the points in a plane and ordered pairs of real numbers; or an association between the points in threedimensional space and ordered triples of real numbers

Common logarithm
A logarithm with base 10.

Expanded form
The right side of u(v + w) = uv + uw.

Horizontal line
y = b.

Integers
The numbers . . ., 3, 2, 1, 0,1,2,...2

Inverse tangent function
The function y = tan1 x

Lemniscate
A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.

Matrix element
Any of the real numbers in a matrix

Multiplicative inverse of a real number
The reciprocal of b, or 1/b, b Z 0

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

Opens upward or downward
A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.

Partial sums
See Sequence of partial sums.

Period
See Periodic function.

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

Quadratic function
A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.

Rational zeros
Zeros of a function that are rational numbers.

Remainder polynomial
See Division algorithm for polynomials.

Sinusoid
A function that can be written in the form f(x) = a sin (b (x  h)) + k or f(x) = a cos (b(x  h)) + k. The number a is the amplitude, and the number h is the phase shift.

System
A set of equations or inequalities.