- 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
Additive inverse of a complex number
The opposite of a + bi, or -a - bi
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots
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.
Points that satisfy the constraints in a linear programming problem.
First-degree 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.
The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.
tan ?= sin ?cos ?and cot ?= cos ? sin ?
See Division algorithm for polynomials.
Behavior that is determined only by the laws of probability.
Semiperimeter of a triangle
One-half of the sum of the lengths of the sides of a triangle.
See Finite sequence, Infinite sequence.
Terms of a sequence
The range elements of a sequence.
A vector that specifies the motion of an object in terms of its speed and direction.
Vertical stretch or shrink
See Stretch, Shrink.