Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Given \(\mathbf{F} = \langle 4yz, 4xz + 2, 4xy + 2x \rangle\), find a function \( f \) such that \(\mathbf{F} = \nabla f\). \[ f(x, y, z) = \underline{\hspace{2cm}} + K \] Use your answer to evaluate \(\int_C \mathbf{F} \cdot d\mathbf{r}\) along the curve \(C: x = t^2, y = t + 4, z = 2t - 4\), \(0 < t \leq 2\). \[ \underline{\hspace{8cm}} \] Question Help: ![Video Icon] Submit Question
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Transcribed Image Text:Given \(\mathbf{F} = \langle 4yz, 4xz + 2, 4xy + 2x \rangle\), find a function \( f \) such that \(\mathbf{F} = \nabla f\). \[ f(x, y, z) = \underline{\hspace{2cm}} + K \] Use your answer to evaluate \(\int_C \mathbf{F} \cdot d\mathbf{r}\) along the curve \(C: x = t^2, y = t + 4, z = 2t - 4\), \(0 < t \leq 2\). \[ \underline{\hspace{8cm}} \] Question Help: ![Video Icon] Submit Question
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