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# Solutions for Chapter 2.4: Applications of the Supremum Property

## Full solutions for Introduction to Real Analysis | 3rd Edition

ISBN: 9780471321484

Solutions for Chapter 2.4: Applications of the Supremum Property

Solutions for Chapter 2.4
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##### ISBN: 9780471321484

This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. Chapter 2.4: Applications of the Supremum Property includes 18 full step-by-step solutions. Since 18 problems in chapter 2.4: Applications of the Supremum Property have been answered, more than 6328 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Absolute value of a real number

Denoted by |a|, represents the number a or the positive number -a if a < 0.

• Aphelion

The farthest point from the Sun in a planet’s orbit

• artesian coordinate system

An association between the points in a plane and ordered pairs of real numbers; or an association between the points in three-dimensional space and ordered triples of real numbers

• Correlation coefficient

A measure of the strength of the linear relationship between two variables, pp. 146, 162.

• Determinant

A number that is associated with a square matrix

• 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>

• Equal complex numbers

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

• Expanded form of a series

A series written explicitly as a sum of terms (not in summation notation).

• Graph of an equation in x and y

The set of all points in the coordinate plane corresponding to the pairs x, y that are solutions of the equation.

• Hypotenuse

Side opposite the right angle in a right triangle.

• Inequality symbol or

<,>,<,>.

• Mathematical model

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

• Mode of a data set

The category or number that occurs most frequently in the set.

• Odd-even identity

For a basic trigonometric function f, an identity relating f(x) to f(-x).

• Open interval

An interval that does not include its endpoints.

• Parabola

The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

• Plane in Cartesian space

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

• 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.

• Union of two sets A and B

The set of all elements that belong to A or B or both.

• Upper bound for real zeros

A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.

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