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# Solutions for Chapter 3.6: Properly Divergent Sequences

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

ISBN: 9780471321484

Solutions for Chapter 3.6: Properly Divergent Sequences

Solutions for Chapter 3.6
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##### ISBN: 9780471321484

Chapter 3.6: Properly Divergent Sequences includes 10 full step-by-step solutions. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. Since 10 problems in chapter 3.6: Properly Divergent Sequences have been answered, more than 2052 students have viewed full step-by-step solutions from this chapter. 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 minimum

A value ƒ(c) is an absolute minimum value of ƒ if ƒ(c) ? ƒ(x)for all x in the domain of ƒ.

• 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 ratio

See Geometric sequence.

• 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)

• Exponential function

A function of the form ƒ(x) = a ? bx,where ?0, b > 0 b ?1

• Five-number summary

The minimum, first quartile, median, third quartile, and maximum of a data set.

• Infinite sequence

A function whose domain is the set of all natural numbers.

• Interval

Connected subset of the real number line with at least two points, p. 4.

• Limit to growth

See Logistic growth function.

• Mathematical induction

A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

• Modified boxplot

A boxplot with the outliers removed.

• Order of an m x n matrix

The order of an m x n matrix is m x n.

• Power rule of logarithms

logb Rc = c logb R, R 7 0.

• Pythagorean

Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

• Range screen

See Viewing window.

• Removable discontinuity at x = a

lim x:a- ƒ(x) = limx:a+ ƒ(x) but either the common limit is not equal ƒ(a) to ƒ(a) or is not defined

• Root of a number

See Principal nth root.

• Sequence

See Finite sequence, Infinite sequence.

A graph in which (-x, y) is on the graph whenever (x, y) is; or a graph in which (-r, -?) or (r, ?, -?) is on the graph whenever (r, ?) is

• z-coordinate

The directed distance from the xy-plane to a point in space, or the third number in an ordered triple.

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