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# Solutions for Chapter 11.4: Metric Spaces

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

ISBN: 9780471321484

Solutions for Chapter 11.4: Metric Spaces

Solutions for Chapter 11.4
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##### ISBN: 9780471321484

This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 11.4: Metric Spaces includes 12 full step-by-step solutions. Since 12 problems in chapter 11.4: Metric Spaces have been answered, more than 8125 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Additive inverse of a complex number

The opposite of a + bi, or -a - bi

• Causation

A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable

• Constraints

See Linear programming problem.

• Exponential decay function

Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

• Focal length of a parabola

The directed distance from the vertex to the focus.

• Imaginary part of a complex number

See Complex number.

• Integrable over [a, b] Lba

ƒ1x2 dx exists.

• Irrational zeros

Zeros of a function that are irrational numbers.

• Mode of a data set

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

• nth root

See Principal nth root

• Ordinary annuity

An annuity in which deposits are made at the same time interest is posted.

• Plane in Cartesian space

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

• Positive association

A relationship between two variables in which higher values of one variable are generally associated with higher values of the other variable, p. 717.

• Projection of u onto v

The vector projv u = au # vƒvƒb2v

• Quartic regression

A procedure for fitting a quartic function to a set of data.

• Reflection across the y-axis

x, y and (-x,y) are reflections of each other across the y-axis.

• Remainder theorem

If a polynomial f(x) is divided by x - c , the remainder is ƒ(c)

• Subtraction

a - b = a + (-b)

• Time plot

A line graph in which time is measured on the horizontal axis.

• Transformation

A function that maps real numbers to real numbers.

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