 5.4.1: Show that the function l(x) := 1/x is uniformly continuous on the s...
 5.4.2: Show that the function l(x) := 1/x2 is uniformly continuous on A :=...
 5.4.3: Use the Nonuniform Continuity Criterion 5.4.2 to show that the foll...
 5.4.4: Show that the function l(x) := 1/(1 + x 2 ) for x e lR is uniformly...
 5.4.5: Show that if I and g are uniformly continuous on a subset A of R, t...
 5.4.6: Show that if I and g are uniformly continuous on A~ lR and if they ...
 5.4.7: If l(x) := x and g(x) := sinx, show that both I and g are uniformly...
 5.4.8: Prove that if I and g are each uniformly continuous on R, then the ...
 5.4.9: H 1 is uniformly continuous on A~ R, and ll(x)l ~ k > 0 for all x e...
 5.4.10: Prove that if I is uniformly continuous on a bounded subset A of R,...
 5.4.11: Hg(x) := ,Jiforx e [0, 1],showthattheredoesnotexistaconstantKsuchth...
 5.4.12: Show that if I is continuous on [0, oo) and uniformly continuous on...
 5.4.13: Let A ~ R and suppose that 1 : A ~ R has the following .property: f...
 5.4.14: A function I: R ~ R is said to be periodic on R if there exists a n...
 5.4.15: If / 0(x) := 1 for x e [0, 1], calculate the first few Bernstein po...
 5.4.16: If / 1 (x) := x for x e [0, 1], calculate the first few Bernstein p...
 5.4.17: If / 2(x) := x 2 for x e [0, 1], calculate the first few Bernstein ...
Solutions for Chapter 5.4: Uniform Continuity
Full solutions for Introduction to Real Analysis  3rd Edition
ISBN: 9780471321484
Solutions for Chapter 5.4: Uniform Continuity
Get Full SolutionsThis 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. Since 17 problems in chapter 5.4: Uniform Continuity have been answered, more than 9461 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.4: Uniform Continuity includes 17 full stepbystep solutions.

Additive inverse of a complex number
The opposite of a + bi, or a  bi

Algebraic expression
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

Arctangent function
See Inverse tangent function.

equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)

Factoring (a polynomial)
Writing a polynomial as a product of two or more polynomial factors.

Feasible points
Points that satisfy the constraints in a linear programming problem.

Firstdegree equation in x , y, and z
An equation that can be written in the form.

Frequency table (in statistics)
A table showing frequencies.

Graph of a function ƒ
The set of all points in the coordinate plane corresponding to the pairs (x, ƒ(x)) for x in the domain of ƒ.

Integrable over [a, b] Lba
ƒ1x2 dx exists.

Partial fractions
The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.

Quotient identities
tan ?= sin ?cos ?and cot ?= cos ? sin ?

Quotient polynomial
See Division algorithm for polynomials.

Random behavior
Behavior that is determined only by the laws of probability.

Second quartile
See Quartile.

Semiperimeter of a triangle
Onehalf of the sum of the lengths of the sides of a triangle.

Sequence
See Finite sequence, Infinite sequence.

Terms of a sequence
The range elements of a sequence.

Velocity
A vector that specifies the motion of an object in terms of its speed and direction.

Vertical stretch or shrink
See Stretch, Shrink.