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# Solutions for Chapter 14.4: GRADIENTS AND DIRECTIONAL DERIVATIVES IN THE PLANE

## Full solutions for Calculus: Single and Multivariable | 6th Edition

ISBN: 9780470888612

Solutions for Chapter 14.4: GRADIENTS AND DIRECTIONAL DERIVATIVES IN THE PLANE

Solutions for Chapter 14.4
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##### ISBN: 9780470888612

This expansive textbook survival guide covers the following chapters and their solutions. Chapter 14.4: GRADIENTS AND DIRECTIONAL DERIVATIVES IN THE PLANE includes 111 full step-by-step solutions. Since 111 problems in chapter 14.4: GRADIENTS AND DIRECTIONAL DERIVATIVES IN THE PLANE have been answered, more than 42184 students have viewed full step-by-step solutions from this chapter. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612. This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6.

Key Calculus Terms and definitions covered in this textbook
• Average velocity

The change in position divided by the change in time.

• Compounded monthly

See Compounded k times per year.

• Directed line segment

See Arrow.

• Exponential regression

A procedure for fitting an exponential function to a set of data.

• Finite sequence

A function whose domain is the first n positive integers for some fixed integer n.

• 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

• Increasing on an interval

A function ƒ is increasing on an interval I if, for any two points in I, a positive change in x results in a positive change in.

• Inductive step

See Mathematical induction.

• Limaçon

A graph of a polar equation r = a b sin u or r = a b cos u with a > 0 b > 0

• Logarithmic form

An equation written with logarithms instead of exponents

• One-to-one function

A function in which each element of the range corresponds to exactly one element in the domain

• 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.

• Random variable

A function that assigns real-number values to the outcomes in a sample space.

• Rational function

Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.

• Second

Angle measure equal to 1/60 of a minute.

• Semimajor axis

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

• Shrink of factor c

A transformation of a graph obtained by multiplying all the x-coordinates (horizontal shrink) by the constant 1/c or all of the y-coordinates (vertical shrink) by the constant c, 0 < c < 1.

• Speed

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

• Variation

See Power function.

• yz-plane

The points (0, y, z) in Cartesian space.

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