Divergence

Practice Questions

Calculus 3 › Divergence

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1

Find the divergence of the vector $\left \langle x^2y^2z^2,3y^5,17z\right \rangle$

2

Given the vector field

$\vec{F}=yz\vec{i}+xz\vec{j}+xy\vec{k}$

find the divergence of the vector field:

$div \vec{F}$ .

3

Find the divergence of the following vector field:

$\vec{F}=\left \langle 7e^{3x}, 2yz, y^3\right \rangle$

4

Find the divergence of the following vector: $\left \langle yz^3,xy^5z,3xz\right \rangle$

5

Find $div \vec{F}$ , where F is given by

$\left \langle x^2z, z^2, ye^xz\right \rangle$

6

Find $div \vec{F}$ of the vector function below:

$\vec{F}=\cos(x)\hat{i}+(xyz)\hat{j}+z^2\sin(y)\hat{k}$

7

Given that F is a vector function and f is a scalar function, which of the following operations results in a vector?

8

Find the divergence of the following vector field:

$\vec{F}=\left \langle xy,yz, \cos(z)\right \rangle$

9

Find the divergence of the vector $\left \langle \cos(x),-2\sin(y),x^2y^2z^2\right \rangle$

10

Find the divergence of the vector field:

$\vec{F}=\left \langle \tan(x^2z), y^2, xy\right \rangle$

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