Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Gradient of a Scalar Field
Consider a room or a place where the temperature is denoted by a scalar field T, such that at each point (x, y, z), the temperature is given as T(x, y, z). It is independent of time, in which the temperature rises most quickly. The gradient of T will sho…
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What will be the magnitude of the gradient of the function f(x,y,z)=x3+y2+z4at the point M(1,1,1)?

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Step 1

In Cartesian coordinate, the gradient of any function f(x,y,z) is expressed as

Electrical Engineering homework question answer, step 1, image 1
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Step 2

In this case, the expression of the function f(x,y,z) is given as

Electrical Engineering homework question answer, step 2, image 1
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Step 3

So, using equation (1), the gradient of the given function will be

Electrical Engineering homework question answer, step 3, image 1
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