 11.2.1: Exhibit an open cover of the interval (1, 2] that has no finite sub...
 11.2.2: Exhibit an open cover of N that has no finite subcover.
 11.2.3: Exhibit an open cover of the set {I/ n: n e N}that has no finite su...
 11.2.4: Prove, using Definition 11.2.2, that if F is a closed subset of a c...
 11.2.5: Prove, using Definition 11.2.2, that if K1and K2 are compact sets i...
 11.2.6: Use the HeineBorel Theorem to prove the following version of the B...
 11.2.7: Find an infinite collection {Kn : n E N} of compact sets in JRsuch ...
 11.2.8: Prove that the intersection of an arbitrary collection of compact s...
 11.2.9: Let (Kn : n E N) be a sequence of nonempty compact sets in JRsuch t...
 11.2.10: Let K :f:0 be a compact set in IR.Show that inf K and sup K exist a...
 11.2.11: Let K :f: 0 be compactin IRand let e E JR.Prove that there exists a...
 11.2.12: Let K :f:0 be compact in JRand let e E IR.Prove that there exists a...
 11.2.13: Use the notion of compactness to give an alternative proof of Exerc...
 11.2.14: If K, and K2 are disjoint nonempty compact sets, show that there ex...
 11.2.15: Give an example of disjoint closed sets Fl' F2 such that 0 = inf{lx...
Solutions for Chapter 11.2: Compact Sets
Full solutions for Introduction to Real Analysis  3rd Edition
ISBN: 9780471321484
Solutions for Chapter 11.2: Compact Sets
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their 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. Since 15 problems in chapter 11.2: Compact Sets have been answered, more than 3155 students have viewed full stepbystep solutions from this chapter. Chapter 11.2: Compact Sets includes 15 full stepbystep solutions.

Angular speed
Speed of rotation, typically measured in radians or revolutions per unit time

Binomial probability
In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n  k2!pk11  p) nk where p is the probability of the outcome occurring once

Bounded interval
An interval that has finite length (does not extend to ? or ?)

Closed interval
An interval that includes its endpoints

Cosine
The function y = cos x

Coterminal angles
Two angles having the same initial side and the same terminal side

Demand curve
p = g(x), where x represents demand and p represents price

Equivalent arrows
Arrows that have the same magnitude and direction.

Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.

Logistic regression
A procedure for fitting a logistic curve to a set of data

Partial fraction decomposition
See Partial fractions.

Power rule of logarithms
logb Rc = c logb R, R 7 0.

Pseudorandom numbers
Computergenerated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random

Pythagorean
Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

Quartic function
A degree 4 polynomial function.

Regression model
An equation found by regression and which can be used to predict unknown values.

Solve by substitution
Method for solving systems of linear equations.

Transformation
A function that maps real numbers to real numbers.

Viewing window
The rectangular portion of the coordinate plane specified by the dimensions [Xmin, Xmax] by [Ymin, Ymax].

Work
The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.
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