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answer to #10 please J18 Determine whether or not the vecto If it is conservativ

ID: 3281619 • Letter: A

Question

answer to #10 please

J18 Determine whether or not the vecto If it is conservative, find a function f such (arctantxy, aretantyz), arctan(zx)) e field F is shown in the xy-plane and looks the 14. Fxaxy+x'y by c other horizontal planes. (In other words, F is ind epen- 15, F(x, y, z) = z dent of z and its 2-component is 0.) t div F positive, negative, or zero? Explain, 16, F(x, y, z) = i + sin zj +ycos 17. F(x, y, z) = e"i + xze" j + , 18. F(x, y, z)= e'sinyz + zero whether curl F 0. If not, in which direction does b) curl F point? 10. y 1 1I/ 19. Is there a vector field G on curl G xsin y,cos y,z -20. Is there a vector field G Explain. 21. Show that any vector fie F(x, y, z) = 11. yt

Explanation / Answer

Two key concepts in vector calculus are divergence and curl, the latter of which is sometimes called circulation.   Basically, divergence has to do with how a vector field changes its magnitude in the neighborhood of a point, and curl has to do with how its direction changes.   Look at the graph of Field 10 below.  It has positive divergence because it has change in magnitude in the neighborhood of every point.(first small arrow and then large arrow)

And now for curl,there is a direction change in the arrow and curl pointing outward .