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All Textbook Solutions for Calculus (MindTap Course List)

Verifying Stokess Theorem In Exercises 3-6, verify Stokess Theorem by evaluating CFdr as a line integral and as a double integral. F(x,y,z)=(y+z)i+(xz)j+(xy)kS:z=1x2y2Verifying Stokess Theorem In Exercises 3-6, verify Stokess Theorem by evaluating CFdr as a line integral and as a double integral. F(x,y,z)=xyzi+yj+zkS:6x+6y+z=12,firstoctantVerifying Stokes Theorem In Exercises 3-6, verify Stokes Theorem by evaluating cFdr as a line integral and as a double integral. F(x,y,z)=z2i+x2j+y2k S:z=y2, 0xa, 0ya7E8E9E10E11EUsing Stokess TheoremIn Exercises 716, use Stokess Theorem to evaluate CFdr. In each case, C is oriented counterclockwise as viewed from above. F(x,y,z)=x2i+z2jxyzkS:z=4x2y2Using Stokess Theorem In Exercises 7-16, use Stokess Theorem to evaluate CFdr . In each case, C is oriented counterclockwise as viewed from above. F(x,y,z)=lnx2+y2i+arctanxyj+k S:z=92x3y over r=2sin2 in the first octantUsing Stokess Theorem In Exercises 7-16, use Stokess Theorem to evaluate CFdr . In each case, C is oriented counterclockwise as viewed from above. F(x,y,z)=yzi+(23y)j+(x2+y2)k,x2+y216S:thefirst-octantprotionofx2+z2=16overx2+y2=16Using Stokes Theorem In Exercises 7-16, use Stokes Theorem to evaluate cFdr. In each case, C is oriented counterclockwise as viewed from above. F(x,y,z)=xyzi+yj+zk S: z=x2, 0xa, 0yaUsing Stokes Theorem In Exercises 7-16, use Stokes Theorem to evaluate cFdr. In each case, C is oriented counterclockwise as viewed from above. F(x,y,z)=xyzi+yj+zk, x2+y2a2 S: the first-octant portion of z=x2 over x2+y2=a2Motion of a Liquid In Exercises 17 and 18, the motion of a liquid in a cylindrical container of radius 3 is described by the vector field F(x,y,z). Find S(curlF)NdS, where S is the upper surface of the cylindrical container. F(x,y,z)=16y3i+16x3j+5kMotion of a Liquid In Exercises 17 and 18, the motion of a liquid in a cylindrical container of radius 3 is described by the velocity field F(x, y, z). Find S(curlF)NdS, where S is the upper surface of the cylindrical container. F(x,y,z)=zi+y2k19EHOW DO YOU SEE IT? Let S1 be the portion of the paraboloid lying above the xy-plane, and let S2 be the hemisphere, as shown in the figures. Both surfaces are oriented upward. For a vector field F(x,y,z) with continuous partial derivatives, does S1(curlF).NdS1=S2(curlF).NdS2? Explain your reasoning.21E
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