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# Solutions for Chapter 11.9: ANALYZING THE PHASE PLANE ## Full solutions for Calculus: Single Variable | 6th Edition

ISBN: 9780470888643 Solutions for Chapter 11.9: ANALYZING THE PHASE PLANE

Solutions for Chapter 11.9
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##### ISBN: 9780470888643

Calculus: Single Variable was written by and is associated to the ISBN: 9780470888643. Since 28 problems in chapter 11.9: ANALYZING THE PHASE PLANE have been answered, more than 32489 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Single Variable , edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 11.9: ANALYZING THE PHASE PLANE includes 28 full step-by-step solutions.

Key Calculus Terms and definitions covered in this textbook
• Cardioid

A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.

• Common logarithm

A logarithm with base 10.

• Data

Facts collected for statistical purposes (singular form is datum)

• Domain of validity of an identity

The set of values of the variable for which both sides of the identity are defined

• 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

• Equation

A statement of equality between two expressions.

• Fibonacci sequence

The sequence 1, 1, 2, 3, 5, 8, 13, . . ..

• Inductive step

See Mathematical induction.

• Lemniscate

A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.

• Line graph

A graph of data in which consecutive data points are connected by line segments

• Random numbers

Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

• Reciprocal function

The function ƒ(x) = 1x

• Right angle

A 90° angle.

• Rigid transformation

A transformation that leaves the basic shape of a graph unchanged.

• Statistic

A number that measures a quantitative variable for a sample from a population.

• Statute mile

5280 feet.

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

• Tangent

The function y = tan x

• Vertex of a cone

See Right circular cone.

• Vertical asymptote

The line x = a is a vertical asymptote of the graph of the function ƒ if limx:a+ ƒ1x2 = q or lim x:a- ƒ1x2 = q.

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