 5.3.1: Let I := [a. b 1 and let I : I ~ lR be a continuous function such t...
 5.3.2: Let I := [a. b 1 and let I : I ~ lR and g : I ~ 1R be continuous fu...
 5.3.3: Let I := [a. b 1 and let I : I ~ lR be a continuous function on I s...
 5.3.4: Show that every polynomial of odd degree with real coefficients has...
 5.3.5: Show that the polynomial p(x) := x 4 + 7x 3  9 has at least two re...
 5.3.6: Let f be continuous on the interval [0, 1] to 1R and such that 1(0)...
 5.3.7: Show that the equation x = cos x has a solution in the interval [0,...
 5.3.8: Show that the function f (x) := 2ln x + ../X  2 has root in the in...
 5.3.9: (a) The function l(x) := (x 1)(x  2)(x  3)(x  4)(x  5) has fiv...
 5.3.10: If the Bisection Method is used on an interval of length 1 to find ...
 5.3.11: Let I := [a, b], let f : I ~ R be continuous on I, and assume that ...
 5.3.12: Let I := [0, 7r/2] and let f: I~ R be defined by f(x) := sup{x2, co...
 5.3.13: Suppose that f: R ~ R is continuous on Rand that lim f = 0 and lim ...
 5.3.14: Let f: R ~ R be continuous on Rand let fJ e R. Show that if x0 e R ...
 5.3.15: Examine which open [respectively, closed] intervals are mapped by f...
 5.3.16: Examine the mapping of open [respectively, closed] intervals under ...
 5.3.17: If f : [0, 1] ~ R is continuous and has only rational [respectively...
 5.3.18: Let I := [a, b] and let I : I ~ R be a (not necessarily continuous)...
 5.3.19: Let J :=(a, b) and let g: J ~ R be a continuous function with the p...
Solutions for Chapter 5.3: Continuous Functions on Intervals
Full solutions for Introduction to Real Analysis  3rd Edition
ISBN: 9780471321484
Solutions for Chapter 5.3: Continuous Functions on Intervals
Get Full SolutionsIntroduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. 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. Chapter 5.3: Continuous Functions on Intervals includes 19 full stepbystep solutions. Since 19 problems in chapter 5.3: Continuous Functions on Intervals have been answered, more than 6953 students have viewed full stepbystep solutions from this chapter.

Ambiguous case
The case in which two sides and a nonincluded angle can determine two different triangles

Average rate of change of ƒ over [a, b]
The number ƒ(b)  ƒ(a) b  a, provided a ? b.

Average velocity
The change in position divided by the change in time.

Center
The central point in a circle, ellipse, hyperbola, or sphere

Completing the square
A method of adding a constant to an expression in order to form a perfect square

Compounded annually
See Compounded k times per year.

Constant function (on an interval)
ƒ(x 1) = ƒ(x 2) x for any x1 and x2 (in the interval)

Difference of two vectors
<u1, u2>  <v1, v2> = <u1  v1, u2  v2> or <u1, u2, u3>  <v1, v2, v3> = <u1  v1, u2  v2, u3  v3>

Directed line segment
See Arrow.

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

Fitting a line or curve to data
Finding a line or curve that comes close to passing through all the points in a scatter plot.

Implied domain
The domain of a function’s algebraic expression.

Inequality
A statement that compares two quantities using an inequality symbol

Natural numbers
The numbers 1, 2, 3, . . . ,.

Ordered pair
A pair of real numbers (x, y), p. 12.

Pascal’s triangle
A number pattern in which row n (beginning with n = 02) consists of the coefficients of the expanded form of (a+b)n.

Polar form of a complex number
See Trigonometric form of a complex number.

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

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

Venn diagram
A visualization of the relationships among events within a sample space.