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# Solutions for Chapter 8: Differential Equations

## Full solutions for Calculus:Early Transcendentals | 7th Edition

ISBN: 9780131569898

Solutions for Chapter 8: Differential Equations

Solutions for Chapter 8
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##### ISBN: 9780131569898

Summary of Chapter 8: Differential Equations

A differential equation is an equation that relates one or more unknown functions and their derivatives. Slope fields and approximate numerical solutions.

Chapter 8: Differential Equations includes 83 full step-by-step solutions. This textbook survival guide was created for the textbook: Calculus:Early Transcendentals, edition: 7. Calculus:Early Transcendentals was written by and is associated to the ISBN: 9780131569898. Since 83 problems in chapter 8: Differential Equations have been answered, more than 40425 students have viewed full step-by-step solutions from this chapter. 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 complex number

The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.

• Complex number

An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers

• Coterminal angles

Two angles having the same initial side and the same terminal side

• Direction of an arrow

The angle the arrow makes with the positive x-axis

• Elimination method

A method of solving a system of linear equations

• Horizontal Line Test

A test for determining whether the inverse of a relation is a function.

• Least-squares line

See Linear regression line.

• Maximum r-value

The value of |r| at the point on the graph of a polar equation that has the maximum distance from the pole

• Outliers

Data items more than 1.5 times the IQR below the first quartile or above the third quartile.

• Parametric equations for a line in space

The line through P0(x 0, y0, z 0) in the direction of the nonzero vector v = <a, b, c> has parametric equations x = x 0 + at, y = y 0 + bt, z = z0 + ct.

• Piecewise-defined function

A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

• Probability simulation

A numerical simulation of a probability experiment in which assigned numbers appear with the same probabilities as the outcomes of the experiment.

• Quotient rule of logarithms

logb a R S b = logb R - logb S, R > 0, S > 0

• Randomization

The principle of experimental design that makes it possible to use the laws of probability when making inferences.

• Reflexive property of equality

a = a

• Simple harmonic motion

Motion described by d = a sin wt or d = a cos wt

• Solve by substitution

Method for solving systems of linear equations.

• Sphere

A set of points in Cartesian space equally distant from a fixed point called the center.

• Triangular number

A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

• xy-plane

The points x, y, 0 in Cartesian space.