 11.3.1: Let I: JR~ JRbe defined by I(x) =x2 for x e R(a) Showthat the inver...
 11.3.2: Let I: JR~ JRbe defined by I(x) := 1/(1 + x2) for x e R(a) Find an ...
 11.3.3: Let 1 := [1, 00) andlet I(x) :=.JX=l for x e I. For eachEneighborh...
 11.3.4: Let h : JR~ JRbe definedby h(x) := 1if 0 ~ x ~ I, h(x) := 0 otherwi...
 11.3.5: Show that if I : JR~ JRis continuous, then the set (x e JR: I(x) < ...
 11.3.6: Showthat if I: JR~ JRis continuous,thenthe set (x e JR:I(x) ~ a} is...
 11.3.7: Show that if I : JR~ JRis continuous, then the set (x e JR: I(x) = ...
 11.3.8: Give an example of a function I : JR~ JRsuch that the set (x e JR: ...
 11.3.9: Prove that I : JR~ JRis continuous if and only if for each closed s...
 11.3.10: Let I := [a, b] and let I : I ~ JRand g : I ~ JRbe continuous funct...
Solutions for Chapter 11.3: Continuous Functions
Full solutions for Introduction to Real Analysis  3rd Edition
ISBN: 9780471321484
Solutions for Chapter 11.3: Continuous Functions
Get Full SolutionsSince 10 problems in chapter 11.3: Continuous Functions have been answered, more than 6282 students have viewed full stepbystep solutions from this chapter. This 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. Chapter 11.3: Continuous Functions includes 10 full stepbystep solutions.

Boundary
The set of points on the “edge” of a region

Differentiable at x = a
ƒ'(a) exists

Elements of a matrix
See Matrix element.

Ellipsoid of revolution
A surface generated by rotating an ellipse about its major axis

Equal complex numbers
Complex numbers whose real parts are equal and whose imaginary parts are equal.

Exponential function
A function of the form ƒ(x) = a ? bx,where ?0, b > 0 b ?1

Higherdegree polynomial function
A polynomial function whose degree is ? 3

Imaginary unit
The complex number.

Irrational zeros
Zeros of a function that are irrational numbers.

Main diagonal
The diagonal from the top left to the bottom right of a square matrix

Mode of a data set
The category or number that occurs most frequently in the set.

Order of an m x n matrix
The order of an m x n matrix is m x n.

Parametric equations
Equations of the form x = ƒ(t) and y = g(t) for all t in an interval I. The variable t is the parameter and I is the parameter interval.

Probability of an event in a finite sample space of equally likely outcomes
The number of outcomes in the event divided by the number of outcomes in the sample space.

Radius
The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).

Reference angle
See Reference triangle

Resistant measure
A statistical measure that does not change much in response to outliers.

Slant asymptote
An end behavior asymptote that is a slant line

symmetric about the xaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Unit circle
A circle with radius 1 centered at the origin.