## Related questions with answers

Question

In given problem, find div $\mathbf{F}$ and curl $\mathbf{F}$.

$\mathbf{F}(x, y, z)=e^x \cos y \mathbf{i}+e^x \sin y \mathbf{j}+z \mathbf{k}$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 3$\begin{align*} \nabla\cdot\mathbf{F} &= \left\langle\dfrac{\partial}{\partial x},\dfrac{\partial}{\partial y},\dfrac{\partial}{\partial z}\right\rangle \cdot \left\langle M,N,P\right\rangle\\ &= \dfrac{\partial M}{\partial x} + \dfrac{\partial N}{\partial y} + \dfrac{\partial P}{\partial z}\\ &=\dfrac{\partial}{\partial x}(e^x\cos y)+\dfrac{\partial}{\partial y}(e^x\sin y)+\dfrac{\partial}{\partial z}(z)\\ &=e^x\cos y+e^x\cos y+1\\ &=2e^x\cos y+1 \end{align*}$

Calculate the divergence of $\mathbf{F}$.

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