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# Solutions for Chapter 5.7: Numerical Approximations of Multiple Integrals (optional) ## Full solutions for Vector Calculus | 4th Edition

ISBN: 9780321780652 Solutions for Chapter 5.7: Numerical Approximations of Multiple Integrals (optional)

Solutions for Chapter 5.7
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##### ISBN: 9780321780652

Since 26 problems in chapter 5.7: Numerical Approximations of Multiple Integrals (optional) have been answered, more than 12877 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Vector Calculus was written by and is associated to the ISBN: 9780321780652. Chapter 5.7: Numerical Approximations of Multiple Integrals (optional) includes 26 full step-by-step solutions.

Key Calculus Terms and definitions covered in this textbook
• Amplitude

See Sinusoid.

• Angle of depression

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

• Annuity

A sequence of equal periodic payments.

• Combination

An arrangement of elements of a set, in which order is not important

• Common ratio

See Geometric sequence.

• 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

• Equivalent systems of equations

Systems of equations that have the same solution.

• Heron’s formula

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

• Inverse of a matrix

The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.

• Line of travel

The path along which an object travels

• Midpoint (in Cartesian space)

For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b

• Ordinary annuity

An annuity in which deposits are made at the same time interest is posted.

• Outcomes

The various possible results of an experiment.

• Parallelogram representation of vector addition

Geometric representation of vector addition using the parallelogram determined by the position vectors.

• Phase shift

See Sinusoid.

Any one of the four parts into which a plane is divided by the perpendicular coordinate axes.

• Real part of a complex number

See Complex number.

• Removable discontinuity at x = a

lim x:a- ƒ(x) = limx:a+ ƒ(x) but either the common limit is not equal ƒ(a) to ƒ(a) or is not defined

• Rigid transformation

A transformation that leaves the basic shape of a graph unchanged.

• Third quartile

See Quartile.

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