 3.4.1: aiv<:_~ ~~P1e of an unbounded sequence that has a convergent subseq...
 3.4.2: Use the method of Example 3.4.3(b) to show that if 0 < c < 1, then ...
 3.4.3: Let Un) be the Fibonacci sequence of Example 3.I.2(d), and let xn :...
 3.4.4: Show that the following sequences are divergent. (a) (1  (_1)n + l...
 3.4.5: Let X = (xn) and Y = (Yn) be given sequences, and let the "shuffled...
 3.4.6: Let xn := nl/n for n EN. (a) Show that xn+1< xn if and only if (1 +...
 3.4.7: Establishthe convergenceand find the limits of the followingsequences:
 3.4.8: Determine the limits of the following. (a) (3n) 1/2n), (b) ((1 + 1/...
 3.4.9: Suppose that every subsequence of X = (xn) has a subsequence that c...
 3.4.10: Let (xn)be a boundedsequenceand for each n E N let sn := sup{xk:k 2...
 3.4.11: Supposethatxn 2: 0 for all n EN andthat lim(ltxJ exists.Showthat (...
 3.4.12: Show that if (x ) is unbounded', then there exists a subsequence (x...
 3.4.13: If xn := (_1)n In, find the subsequence of (xn) that is constructed...
 3.4.14: Let (xn) be a bounded sequence and let S := sup{xn:n EN}. Show that...
 3.4.15: Let (I n) be a nested sequence of closed bounded intervals. For eac...
 3.4.16: Give an example to show that Theorem 3.4.9 fails if the hypothesis ...
Solutions for Chapter 3.4: Subsequences and the Bolzano Weierstrass Theorem
Full solutions for Introduction to Real Analysis  3rd Edition
ISBN: 9780471321484
Solutions for Chapter 3.4: Subsequences and the Bolzano Weierstrass Theorem
Get Full SolutionsIntroduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. Since 16 problems in chapter 3.4: Subsequences and the Bolzano Weierstrass Theorem have been answered, more than 8641 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3.4: Subsequences and the Bolzano Weierstrass Theorem includes 16 full stepbystep solutions.

Arccosecant function
See Inverse cosecant function.

Axis of symmetry
See Line of symmetry.

Census
An observational study that gathers data from an entire population

Cone
See Right circular cone.

Continuous function
A function that is continuous on its entire domain

Divisor of a polynomial
See Division algorithm for polynomials.

Elementary row operations
The following three row operations: Multiply all elements of a row by a nonzero constant; interchange two rows; and add a multiple of one row to another row

Gaussian elimination
A method of solving a system of n linear equations in n unknowns.

Heron’s formula
The area of ¢ABC with semiperimeter s is given by 2s1s  a21s  b21s  c2.

Horizontal Line Test
A test for determining whether the inverse of a relation is a function.

Inductive step
See Mathematical induction.

Linear programming problem
A method of solving certain problems involving maximizing or minimizing a function of two variables (called an objective function) subject to restrictions (called constraints)

Logarithmic reexpression of data
Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression

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

Major axis
The line segment through the foci of an ellipse with endpoints on the ellipse

Multiplication principle of probability
If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(AB) # P(B)

Standard position (angle)
An angle positioned on a rectangular coordinate system with its vertex at the origin and its initial side on the positive xaxis

Terminal side of an angle
See Angle.

Vertex of a parabola
The point of intersection of a parabola and its line of symmetry.

xzplane
The points x, 0, z in Cartesian space.