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Chapter 14: Q. 28 (page 1096)

Sketch the vector fields in Exercises 25–32.

F(x,y)=2i+2j

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)=2i+2j

02

Step 2. The given vector field F(x,y)=2i+2j

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" ∂R.

  • (a) Compute localid="1650455166518" ∬R∂F2∂x-∂F1∂ydA.
  • (b) Show that∫∂RF·nds=∫02π1.152-0.8cos2θsinθdθ. 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

∫S F(x,y,z)⋅ndSifF(x,y,z)=ln⁡x2+y2+1z+3i+yy+1j+ez2k

Where S is the portion of the sphere with radius 2, centered at the origin, and that lies below the plane with equation z=-2, with n pointing outwards.

Integrate the given function over the accompanying surface in Exercises 27–34.
f(x,y,z)=x2-y+3z, where Sis the portion of the plane with equation 2x-6y+3z=1whose preimage in the xz plane is the region bounded by the coordinate axes and the lines with equations z = 4 and x = z.

Find the areas of the given surfaces in Exercises 21–26.

S is the lower branch of the hyperboloid of two sheets z2=x2+y2+1that lies below the annulus determined by 1≤r≤2 in the xy plane.

Give a formula for a normal vector to the surface S determined by y = g(x,z), where g(x,z) is a function with continuous partial derivatives.
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