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# Solutions for Chapter 2: Differentiation in Several Variables ## Full solutions for Vector Calculus | 4th Edition

ISBN: 9780321780652 Solutions for Chapter 2: Differentiation in Several Variables

Solutions for Chapter 2
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##### ISBN: 9780321780652

This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. Chapter 2: Differentiation in Several Variables includes 44 full step-by-step solutions. Since 44 problems in chapter 2: Differentiation in Several Variables have been answered, more than 13399 students have viewed full step-by-step solutions from this chapter. Vector Calculus was written by and is associated to the ISBN: 9780321780652. This expansive textbook survival guide covers the following chapters and their solutions.

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

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

• Acute triangle

A triangle in which all angles measure less than 90°

• Angle between vectors

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

• Blind experiment

An experiment in which subjects do not know if they have been given an active treatment or a placebo

• Exponential form

An equation written with exponents instead of logarithms.

• Gaussian elimination

A method of solving a system of n linear equations in n unknowns.

• Hyperboloid of revolution

A surface generated by rotating a hyperbola about its transverse axis, p. 607.

• Inverse composition rule

The composition of a one-toone function with its inverse results in the identity function.

• Inverse properties

a + 1-a2 = 0, a # 1a

• Irrational numbers

Real numbers that are not rational, p. 2.

• 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

• Perihelion

The closest point to the Sun in a planet’s orbit.

• Periodic function

A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.

• Polar equation

An equation in r and ?.

• Reciprocal function

The function ƒ(x) = 1x

• Replication

The principle of experimental design that minimizes the effects of chance variation by repeating the experiment multiple times.

• Speed

The magnitude of the velocity vector, given by distance/time.

• Vertices of a hyperbola

The points where a hyperbola intersects the line containing its foci.

• Yscl

The scale of the tick marks on the y-axis in a viewing window.

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