Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. If ▿ · F = 0 at all points of a region D . then F · n = 0 at all points of the boundary of D. b. If ∬ S F ⋅ n d S = 0 on all closed surfaces in ¡ 3 , then F is constant. c. If | F | < 1, then | ∬ D ∇ ⋅ F d V | is less than the area of the surface of D.
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. If ▿ · F = 0 at all points of a region D . then F · n = 0 at all points of the boundary of D. b. If ∬ S F ⋅ n d S = 0 on all closed surfaces in ¡ 3 , then F is constant. c. If | F | < 1, then | ∬ D ∇ ⋅ F d V | is less than the area of the surface of D.
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Prove d(x,y) = 8 if x does not equal y and 0 if x equals y is a metric on R, the real numbers.
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Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY