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# Solutions for Chapter 9: First-Order Differential Equations

## Full solutions for Thomas' Calculus | 12th Edition

ISBN: 9780321587992

Solutions for Chapter 9: First-Order Differential Equations

Solutions for Chapter 9
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##### ISBN: 9780321587992

This expansive textbook survival guide covers the following chapters and their solutions. Chapter 9: First-Order Differential Equations includes 36 full step-by-step solutions. Thomas' Calculus was written by Sieva Kozinsky and is associated to the ISBN: 9780321587992. Since 36 problems in chapter 9: First-Order Differential Equations have been answered, more than 3952 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Thomas' Calculus, edition: 12.

Key Calculus Terms and definitions covered in this textbook
• Blocking

A feature of some experimental designs that controls for potential differences between subject groups by applying treatments randomly within homogeneous blocks of subjects

• Common logarithm

A logarithm with base 10.

• Complex plane

A coordinate plane used to represent the complex numbers. The x-axis of the complex plane is called the real axis and the y-axis is the imaginary axis

• Directrix of a parabola, ellipse, or hyperbola

A line used to determine the conic

• Half-life

The amount of time required for half of a radioactive substance to decay.

• Horizontal asymptote

The line is a horizontal asymptote of the graph of a function ƒ if lim x:- q ƒ(x) = or lim x: q ƒ(x) = b

• Inverse sine function

The function y = sin-1 x

• Linear regression line

The line for which the sum of the squares of the residuals is the smallest possible

• Normal distribution

A distribution of data shaped like the normal curve.

• Odd-even identity

For a basic trigonometric function f, an identity relating f(x) to f(-x).

• Plane in Cartesian space

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

• Pythagorean identities

sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u

The graph in three dimensions of a seconddegree equation in three variables.

• Quotient polynomial

See Division algorithm for polynomials.

• Semiminor axis

The distance from the center of an ellipse to a point on the ellipse along a line perpendicular to the major axis.

• Solve by substitution

Method for solving systems of linear equations.

• Standard form of a polar equation of a conic

r = ke 1 e cos ? or r = ke 1 e sin ? ,

• Tangent

The function y = tan x

• Time plot

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

• Variable

A letter that represents an unspecified number.

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