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# Solutions for Chapter 4.7: Fundamentals of Differential Equations 8th Edition ## Full solutions for Fundamentals of Differential Equations | 8th Edition

ISBN: 9780321747730 Solutions for Chapter 4.7

Solutions for Chapter 4.7
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##### ISBN: 9780321747730

Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. Chapter 4.7 includes 54 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Since 54 problems in chapter 4.7 have been answered, more than 66508 students have viewed full step-by-step solutions from this chapter.

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.

• Angle of depression

The acute angle formed by the line of sight (downward) and the horizontal

• Cosecant

The function y = csc x

• Half-angle identity

Identity involving a trigonometric function of u/2.

• Independent events

Events A and B such that P(A and B) = P(A)P(B)

• Length of a vector

See Magnitude of a vector.

• Lower bound of f

Any number b for which b < ƒ(x) for all x in the domain of ƒ

• 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

• Minor axis

The perpendicular bisector of the major axis of an ellipse with endpoints on the ellipse.

• Multiplication property of equality

If u = v and w = z, then uw = vz

• Natural logarithmic regression

A procedure for fitting a logarithmic curve to a set of data.

• Product rule of logarithms

ogb 1RS2 = logb R + logb S, R > 0, S > 0,

• Relation

A set of ordered pairs of real numbers.

• Right circular cone

The surface created when a line is rotated about a second line that intersects but is not perpendicular to the first line.

• Sinusoid

A function that can be written in the form f(x) = a sin (b (x - h)) + k or f(x) = a cos (b(x - h)) + k. The number a is the amplitude, and the number h is the phase shift.

• Sinusoidal regression

A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

• Unit vector in the direction of a vector

A unit vector that has the same direction as the given vector.

• Vertex form for a quadratic function

ƒ(x) = a(x - h)2 + k

• Vertical translation

A shift of a graph up or down.

• yz-plane

The points (0, y, z) in Cartesian space.

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