14. Divergence Theorem and Final Review

Review And Synthesis — Quiz

Test your understanding of review and synthesis with 5 practice questions.

Practice Questions

Question 1

According to the Divergence Theorem, what is the outward flux through a closed surface equal to?

Question 2

If a vector field is smooth on and inside a closed surface and its divergence is $0$ everywhere in the enclosed region, what is the net outward flux across the surface?

Question 3

What is the divergence of $\mathbf{F}(x,y,z)=\langle x,y,z\rangle$?

Question 4

Which condition must the surface satisfy for the standard Divergence Theorem to apply?

Question 5

Use the Divergence Theorem to find the outward flux of $\mathbf{F}(x,y,z)=\langle 2x,2y,2z\rangle$ across the unit sphere.