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Solutions for Chapter 5: Double and Triple Integrals

Full solutions for Vector Calculus | 6th Edition

ISBN: 9781429215084

Solutions for Chapter 5: Double and Triple Integrals

Solutions for Chapter 5
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ISBN: 9781429215084

Vector Calculus was written by and is associated to the ISBN: 9781429215084. This textbook survival guide was created for the textbook: Vector Calculus, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5: Double and Triple Integrals includes 37 full step-by-step solutions. Since 37 problems in chapter 5: Double and Triple Integrals have been answered, more than 3075 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Absolute maximum

A value ƒ(c) is an absolute maximum value of ƒ if ƒ(c) ? ƒ(x) for all x in the domain of ƒ.

• Arccotangent function

See Inverse cotangent function.

• Binomial coefficients

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

• Differentiable at x = a

ƒ'(a) exists

• Equal complex numbers

Complex numbers whose real parts are equal and whose imaginary parts are equal.

• Heron’s formula

The area of ¢ABC with semiperimeter s is given by 2s1s - a21s - b21s - c2.

• 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

• Imaginary part of a complex number

See Complex number.

• Irrational zeros

Zeros of a function that are irrational numbers.

• Observational study

A process for gathering data from a subset of a population through current or past observations. This differs from an experiment in that no treatment is imposed.

• Position vector of the point (a, b)

The vector <a,b>.

• Quartile

The first quartile is the median of the lower half of a set of data, the second quartile is the median, and the third quartile is the median of the upper half of the data.

• Residual

The difference y1 - (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.

• Sum of functions

(ƒ + g)(x) = ƒ(x) + g(x)

• Tangent

The function y = tan x

• Translation

See Horizontal translation, Vertical translation.

• Tree diagram

A visualization of the Multiplication Principle of Probability.

• Upper bound for real zeros

A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.

• Window dimensions

The restrictions on x and y that specify a viewing window. See Viewing window.

• y-axis

Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.

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