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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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Section
BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

(a) Define the gradient vector ∇f for a function f of two three variables.

(b) Express Duf in terms of ∇f.

(c) Explain the geometric significance of the gradient.

(a)

To determine

To define: The gradient vector f for the function f of two or three variables.

Explanation

Consider the function of two variables, f(x,y) .

The gradient vector of f(x,y) is defined as,

f(x,y)=fxi+fxj=fx,fy

Consider the function of three variables, f(x,y,z)

(b)

To determine

To express: The directional derivative Duf in terms of f .

(c)

To determine

To explain: The geometrical significance of the gradient.

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Chapter 14 Solutions

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