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1 1 1 Calculate the gradient of h(x, y, z)=33 Vh = h (2xi) + 3yj + 3zk

1 1 1 Calculate the gradient of h(x, y, z)=33 Vh = h (2xi) + 3yj + 3zk

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Calculate the Gradient of** \( h(x, y, z) = \frac{1}{x^2} \frac{1}{y^3} \frac{1}{z^3} \) The gradient of \( h \) is given by: \[ \nabla h = h(2x\mathbf{i}) + 3y\mathbf{j} + 3z\mathbf{k} \] Here, the equation describes the process of calculating the gradient of a scalar function \( h(x, y, z) \). The gradient vector is expressed in terms of the unit vectors \(\mathbf{i}\), \(\mathbf{j}\), and \(\mathbf{k}\), indicating the directions of the x, y, and z axes, respectively. The partial derivatives of the function are multiplied by their respective variables and unit vectors to form the gradient.
Transcribed Image Text:**Calculate the Gradient of** \( h(x, y, z) = \frac{1}{x^2} \frac{1}{y^3} \frac{1}{z^3} \) The gradient of \( h \) is given by: \[ \nabla h = h(2x\mathbf{i}) + 3y\mathbf{j} + 3z\mathbf{k} \] Here, the equation describes the process of calculating the gradient of a scalar function \( h(x, y, z) \). The gradient vector is expressed in terms of the unit vectors \(\mathbf{i}\), \(\mathbf{j}\), and \(\mathbf{k}\), indicating the directions of the x, y, and z axes, respectively. The partial derivatives of the function are multiplied by their respective variables and unit vectors to form the gradient.
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