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# Solutions for Chapter 9.2: A First Course in Differential Equations with Modeling Applications 10th Edition

## Full solutions for A First Course in Differential Equations with Modeling Applications | 10th Edition

ISBN: 9781111827052

Solutions for Chapter 9.2

Solutions for Chapter 9.2
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##### ISBN: 9781111827052

Chapter 9.2 includes 21 full step-by-step solutions. This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. This expansive textbook survival guide covers the following chapters and their solutions. Since 21 problems in chapter 9.2 have been answered, more than 48555 students have viewed full step-by-step solutions from this chapter. A First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052.

Key Calculus Terms and definitions covered in this textbook
• Additive inverse of a real number

The opposite of b , or -b

• Arrow

The notation PQ denoting the directed line segment with initial point P and terminal point Q.

• Binomial coefficients

The numbers in Pascal’s triangle: nCr = anrb = n!r!1n - r2!

• Conjugate axis of a hyperbola

The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

• 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

• Elementary row operations

The following three row operations: Multiply all elements of a row by a nonzero constant; interchange two rows; and add a multiple of one row to another row

• equation of an ellipse

(x - h2) a2 + (y - k)2 b2 = 1 or (y - k)2 a2 + (x - h)2 b2 = 1

• Half-plane

The graph of the linear inequality y ? ax + b, y > ax + b y ? ax + b, or y < ax + b.

• Inverse cosecant function

The function y = csc-1 x

• Odd function

A function whose graph is symmetric about the origin (ƒ(-x) = -ƒ(x) for all x in the domain of f).

• Polar coordinates

The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

• Root of a number

See Principal nth root.

• Semimajor axis

The distance from the center to a vertex of an ellipse.

• Slope-intercept form (of a line)

y = mx + b

• Standard form of a polar equation of a conic

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

A graph in which (-x, y) is on the graph whenever (x, y) is; or a graph in which (-r, -?) or (r, ?, -?) is on the graph whenever (r, ?) is

• Tangent line of ƒ at x = a

The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.

• Third quartile

See Quartile.

• Trigonometric form of a complex number

r(cos ? + i sin ?)

• Vector

An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.

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