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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 8641 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
• 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 re-expression 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(A|B) # 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 x-axis

• Terminal side of an angle

See Angle.

• Vertex of a parabola

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

• xz-plane

The points x, 0, z in Cartesian space.

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