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Chapter 14: Q. 32 (page 1096)

Sketch the vector fields in Exercises 25鈥�32.

F(x,y)=-2xi-3yj

Short Answer

Expert verified

Sketch of the vector fields is

Step by step solution

01

Step 1. Given Information

We have to sketch the vector fields in the given exercises .

F(x,y)=-2xi-3yj

02

Step 2. The given vector field F(x,y)=-2xi-3yj

The graph of the vector field is

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Most popular questions from this chapter

The current through a certain passage of the San Juan Islands in Washington State is given by

F=F1(x,y),F2(x,y)=0,1.152-0.8x2.

Consider a disk R of radius 1 mile and centered on this region. Denote the boundary of the disk by localid="1650455155947" 鈭�R.

  • (a) Compute localid="1650455166518" 鈭�R鈭�F2鈭�x-鈭�F1鈭�ydA.
  • (b) Show that鈭�鈭�RF路nds=鈭�02蟺1.152-0.8cos2胃sin胃d胃. Conclude that Green's Theorem is valid for the current in this area of the San Juan Islands.
  • (c) What do the integrals from Green's Theorem tell us about this region of the San Juan Islands?

Find

鈭�S鈥�F(x,y,z)鈰�ndSifF(x,y,z)=2xzi+2yzj鈭�18k

and S is the portion of the hyperboloid x2+y2-9=z2that lies between the planes

z = 鈭�4 and z = 0, with n pointing outwards.

Make a chart of all the new notation, definitions, and theorems in this section, including what each new item means in terms you already understand.

Why do surface integrals of multivariate functions not include an n term, whereas surface integrals of vector fields do include this term?

ComputethecurlofthevectorfieldsinExercises23鈥�28.G(x,y,z)=(x2+y鈭�z)i鈭�2ycoszj+ex2+y2+z2k
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