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# Solutions for Chapter 10.4: Autonomous Systems as Mathematical Models

## Full solutions for Differential Equations with Boundary-Value Problems | 7th Edition

ISBN: 9780495108368

Solutions for Chapter 10.4: Autonomous Systems as Mathematical Models

Solutions for Chapter 10.4
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##### ISBN: 9780495108368

Chapter 10.4: Autonomous Systems as Mathematical Models includes 22 full step-by-step solutions. Since 22 problems in chapter 10.4: Autonomous Systems as Mathematical Models have been answered, more than 15924 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Differential Equations with Boundary-Value Problems, edition: 7. Differential Equations with Boundary-Value Problems was written by and is associated to the ISBN: 9780495108368.

Key Calculus Terms and definitions covered in this textbook
• Back-to-back stemplot

A stemplot with leaves on either side used to compare two distributions.

• Bounded

A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

• Coefficient of determination

The number r2 or R2 that measures how well a regression curve fits the data

• Equation

A statement of equality between two expressions.

• Graph of a polar equation

The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.

• Imaginary axis

See Complex plane.

• Implicitly defined function

A function that is a subset of a relation defined by an equation in x and y.

• Interquartile range

The difference between the third quartile and the first quartile.

See Polynomial function in x

• Left-hand limit of f at x a

The limit of ƒ as x approaches a from the left.

• Lower bound for real zeros

A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

• 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)

• Mean (of a set of data)

The sum of all the data divided by the total number of items

• Opposite

See Additive inverse of a real number and Additive inverse of a complex number.

• Paraboloid of revolution

A surface generated by rotating a parabola about its line of symmetry.

• Point-slope form (of a line)

y - y1 = m1x - x 12.

• Rational numbers

Numbers that can be written as a/b, where a and b are integers, and b ? 0.

• Rectangular coordinate system

See Cartesian coordinate system.

• Stemplot (or stem-and-leaf plot)

An arrangement of a numerical data set into a specific tabular format.

• Vertical translation

A shift of a graph up or down.

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