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# Solutions for Chapter 2.5: Intervals

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

ISBN: 9780471321484

Solutions for Chapter 2.5: Intervals

Solutions for Chapter 2.5
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##### ISBN: 9780471321484

Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. Since 17 problems in chapter 2.5: Intervals have been answered, more than 2615 students have viewed full step-by-step solutions from this chapter. Chapter 2.5: Intervals includes 17 full step-by-step solutions. 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.

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.

• Bounded interval

An interval that has finite length (does not extend to ? or -?)

• Combinations of n objects taken r at a time

There are nCr = n! r!1n - r2! such combinations,

• Components of a vector

See Component form of a vector.

• Constant term

See Polynomial function

• Decreasing on an interval

A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

• Deductive reasoning

The process of utilizing general information to prove a specific hypothesis

• Explanatory variable

A variable that affects a response variable.

• Hypotenuse

Side opposite the right angle in a right triangle.

• Inequality

A statement that compares two quantities using an inequality symbol

• 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.

• Projection of u onto v

The vector projv u = au # vƒvƒb2v

• Proportional

See Power function

• Quotient of complex numbers

a + bi c + di = ac + bd c2 + d2 + bc - ad c2 + d2 i

• Random variable

A function that assigns real-number values to the outcomes in a sample space.

• Rational function

Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.

• Relation

A set of ordered pairs of real numbers.

• Standard form of a polynomial function

ƒ(x) = an x n + an-1x n-1 + Á + a1x + a0

• Xmin

The x-value of the left side of the viewing window,.

• xz-plane

The points x, 0, z in Cartesian space.

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