Advanced Math Archive: Questions from August 15, 2022
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Using some combination of the 8 Basic, the 10 Equivalence, the 2 Subproof the 4 Quantifier, and the QN Rule, construct a proof for each of the following four questions in the spaces provided. Each pro1 answer -
\( \begin{aligned} \mathbf{u r l}(\mathbf{F} \times \mathbf{G}) &=\nabla \times(\mathbf{F} \times \mathbf{G}) \\ \mathbf{F}(x, y, z) &=\mathbf{i}+4 x \mathbf{j}+2 y \mathbf{k} \\ \mathbf{G}(x, y, z) &1 answer -
\( \begin{aligned} \operatorname{div}(\mathbf{F} \times \mathbf{G})=& \nabla \cdot(\mathbf{F} \times \mathbf{G}) \\ \mathbf{F}(x, y, z) &=\mathbf{i}+6 x \mathbf{j}+4 y \mathbf{k} \\ \mathbf{G}(x, y, z1 answer -
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Let \( f(x, y, z)=5 x z e^{4 y z} \). Find \( \frac{\partial f}{\partial x}(x, y, z), \frac{\partial f}{\partial y}(x, y, z) \), and \( \frac{\partial f}{\partial z}(x, y, z) \) \[ \frac{\partial f}{\1 answer -
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