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# 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

Solutions for Chapter 3.4
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##### ISBN: 9780471321484

Introduction 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 3126 students have viewed full step-by-step 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 step-by-step solutions.

Key Calculus Terms and definitions covered in this textbook
• Categorical variable

In statistics, a nonnumerical variable such as gender or hair color. Numerical variables like zip codes, in which the numbers have no quantitative significance, are also considered to be categorical.

• Common difference

See Arithmetic sequence.

• Equivalent arrows

Arrows that have the same magnitude and direction.

• First octant

The points (x, y, z) in space with x > 0 y > 0, and z > 0.

• Frequency

Reciprocal of the period of a sinusoid.

• Function

A relation that associates each value in the domain with exactly one value in the range.

• Integrable over [a, b] Lba

ƒ1x2 dx exists.

• kth term of a sequence

The kth expression in the sequence

• Leaf

The final digit of a number in a stemplot.

• Lemniscate

A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.

• Mathematical model

A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

• Opposite

See Additive inverse of a real number and Additive inverse of a complex number.

• Period

See Periodic function.

• Plane in Cartesian space

The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

• Response variable

A variable that is affected by an explanatory variable.

• Right-hand limit of ƒ at x a

The limit of ƒ as x approaches a from the right.

• Summation notation

The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series

• Triangular number

A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

• Vertex form for a quadratic function

ƒ(x) = a(x - h)2 + k

• yz-plane

The points (0, y, z) in Cartesian space.

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