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Solutions for Chapter 6.1: Fundamentals of Differential Equations 8th Edition

Full solutions for Fundamentals of Differential Equations | 8th Edition

ISBN: 9780321747730

Solutions for Chapter 6.1

Solutions for Chapter 6.1
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ISBN: 9780321747730

Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. Since 35 problems in chapter 6.1 have been answered, more than 61022 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Chapter 6.1 includes 35 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Key Calculus Terms and definitions covered in this textbook
• Dependent event

An event whose probability depends on another event already occurring

• Distance (in Cartesian space)

The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x ) - x 2)2 + (y1 - y2)2 + (z 1 - z 2)2

• Ellipsoid of revolution

A surface generated by rotating an ellipse about its major axis

• Exponential function

A function of the form ƒ(x) = a ? bx,where ?0, b > 0 b ?1

• Finite series

Sum of a finite number of terms.

• Independent events

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

• Length of an arrow

See Magnitude of an arrow.

• Local maximum

A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

• LRAM

A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the left-hand endpoint of each subinterval

• Magnitude of a vector

The magnitude of <a, b> is 2a2 + b2. The magnitude of <a, b, c> is 2a2 + b2 + c2

• Magnitude of an arrow

The magnitude of PQ is the distance between P and Q

• One-to-one function

A function in which each element of the range corresponds to exactly one element in the domain

• Ordered set

A set is ordered if it is possible to compare any two elements and say that one element is “less than” or “greater than” the other.

• Polar equation

An equation in r and ?.

• Polynomial in x

An expression that can be written in the form an x n + an-1x n-1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

• Product rule of logarithms

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

• Remainder polynomial

See Division algorithm for polynomials.

• Scalar

A real number.

• Simple harmonic motion

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

• Vertex of a cone

See Right circular cone.

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