Let F = (6xyz + 2sinx, 3x^2z, 3x^2y). Find a function f so that F = \bigtriangledown f , and f(0,...


Let {eq}F = (6xyz + 2sinx, 3x^2z, 3x^2y) {/eq}. Find a function f so that {eq}F = \bigtriangledown f {/eq}, and f(0, 0, 0) = 0 .

Vector Field:

In this problem, we'll use the gradient theorem:

{eq}\mathbf F= \nabla f = \dfrac{\partial f}{ \partial x } \mathbf i+\dfrac{\partial f}{ \partial y } \mathbf j+\dfrac{\partial f}{ \partial z } \mathbf k {/eq}

Next, we'll integrate interms of {eq}x,y,z {/eq} to get the desired solution.

Answer and Explanation:

We are given:

{eq}\mathbf F(x,y,z)= (6xyz + 2sinx, 3x^2z, 3x^2y) {/eq}

We need to find the scalar potential.

Since {eq}\mathbf F= \nabla f = ...

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from PSAT Prep: Tutoring Solution

Chapter 10 / Lesson 13

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