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Solutions for Chapter 14.6: Directional Derivatives and the Gradient Vector

Full solutions for Calculus: Early Transcendentals | 7th Edition

ISBN: 9780538497909

Solutions for Chapter 14.6: Directional Derivatives and the Gradient Vector

Solutions for Chapter 14.6
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ISBN: 9780538497909

Since 68 problems in chapter 14.6: Directional Derivatives and the Gradient Vector have been answered, more than 33371 students have viewed full step-by-step solutions from this chapter. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780538497909. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 7. Chapter 14.6: Directional Derivatives and the Gradient Vector includes 68 full step-by-step solutions.

Key Calculus Terms and definitions covered in this textbook

If u < v , then u + w < v + w

• Arcsine function

See Inverse sine function.

• Binomial probability

In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n - k2!pk11 - p) n-k where p is the probability of the outcome occurring once

• Boundary

The set of points on the “edge” of a region

• Completing the square

A method of adding a constant to an expression in order to form a perfect square

• Directed angle

See Polar coordinates.

• Double-blind experiment

A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment

• Expanded form

The right side of u(v + w) = uv + uw.

• Horizontal Line Test

A test for determining whether the inverse of a relation is a function.

• Identity matrix

A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.

• Imaginary part of a complex number

See Complex number.

• Linear factorization theorem

A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1 - z1) 1x - i z 22 Á 1x - z n where the z1 are the zeros of ƒ

• Modulus

See Absolute value of a complex number.

• Natural exponential function

The function ƒ1x2 = ex.

• Permutations of n objects taken r at a time

There are nPr = n!1n - r2! such permutations

• Range of a function

The set of all output values corresponding to elements in the domain.

• 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.

• Standard form: equation of a circle

(x - h)2 + (y - k2) = r 2

A graph in which (-x, -y) is on the the graph whenever (x, y) is; or a graph in which (-r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is

• Venn diagram

A visualization of the relationships among events within a sample space.

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