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# Solutions for Chapter 15: MULTIPLE INTEGRATION

## Full solutions for Calculus: Early Transcendentals | 3rd Edition

ISBN: 9781464114885

Solutions for Chapter 15: MULTIPLE INTEGRATION

Solutions for Chapter 15
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##### ISBN: 9781464114885

This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 15: MULTIPLE INTEGRATION includes 61 full step-by-step solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. Since 61 problems in chapter 15: MULTIPLE INTEGRATION have been answered, more than 41868 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Absolute value of a vector

See Magnitude of a vector.

• Algebraic expression

A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

• Anchor

See Mathematical induction.

• Angle between vectors

The angle formed by two nonzero vectors sharing a common initial point

• Average rate of change of ƒ over [a, b]

The number ƒ(b) - ƒ(a) b - a, provided a ? b.

• Coordinate(s) of a point

The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian three-dimensional space

• Factoring (a polynomial)

Writing a polynomial as a product of two or more polynomial factors.

• Half-life

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

• Initial point

See Arrow.

• Integrable over [a, b] Lba

ƒ1x2 dx exists.

• Irreducible quadratic over the reals

A quadratic polynomial with real coefficients that cannot be factored using real coefficients.

• Minor axis

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

• 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.

The formula x = -b 2b2 - 4ac2a used to solve ax 2 + bx + c = 0.

• Reflection across the x-axis

x, y and (x,-y) are reflections of each other across the x-axis.

• Sample survey

A process for gathering data from a subset of a population, usually through direct questioning.

• Semiperimeter of a triangle

One-half of the sum of the lengths of the sides of a triangle.

• Sum of a finite arithmetic series

Sn = na a1 + a2 2 b = n 2 32a1 + 1n - 12d4,

• Sum of a finite geometric series

Sn = a111 - r n 2 1 - r

• Variable (in statistics)

A characteristic of individuals that is being identified or measured.

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