Problem 1RE: Explain why or why not Determine whether the following statements are true and give an explanation... Problem 2RE: Matching vector fields Match vector fields a-f with the graphs A-F. Let r = x, y. a.F = x, y b.F =... Problem 3RE: Gradient fields in 2 Find the vector field F = for the following potential functions. Sketch a few... Problem 4RE: Gradient fields in 2 Find the vector field F = for the following potential functions. Sketch a few... Problem 5RE: Gradient fields in 3 Find the vector field F = for the following potential functions. 5.(x, y, z) =... Problem 6RE: Gradient fields in 3 Find the vector field F = for the following potential functions.... Problem 7RE: Normal component Let C be the circle of radius 2 centered at the origin with counterclockwise... Problem 8RE: Line integrals Evaluate the following line integrals. 8.C(x22xy+y2)ds;C is the upper half of the... Problem 9RE Problem 10RE: Line integrals Evaluate the following line integrals. 10.C(xzy2)ds; C is the line segment from (0,... Problem 11RE: Two parameterizations Verify that C(x2y+3z)ds has the same value when C is given by r(t) = 2 cos t,... Problem 12RE: Work integral Find the work done in moving an object from P(1, 0, 0) to Q(0, 1, 0) in the presence... Problem 13RE: Work integrals in R3 Given the following force fields, find the work required to move an object on... Problem 14RE: Work integrals in 3 Given the following force fields, find the work required to move an object on... Problem 15RE: Circulation and flux Find the circulation and the outward flux of the following vector fields for... Problem 16RE: Circulation and flux Find the circulation and the outward flux of the following vector fields for... Problem 17RE: Circulation and flux Find the circulation and the outward flux of the following vector fields for... Problem 18RE: Circulation and flux Find the circulation and the outward flux of the following vector fields for... Problem 19RE: Flux in channel flow Consider the flow of water in a channel whose boundaries are the planes y = L... Problem 20RE: Conservative vector fields and potentials Determine whether the following vector fields are... Problem 21RE: Conservative vector fields and potentials Determine whether the following vector fields are... Problem 22RE: Conservative vector fields and potentials Determine whether the following vector fields are... Problem 23RE: Conservative vector fields and potentials Determine whether the following vector fields are... Problem 24RE: Evaluating line integrals Evaluate the line integral CFdr for the following vector fields F and... Problem 25RE: Evaluating line integrals Evaluate the line integral CFdr for the following vector fields F and... Problem 26RE: Evaluating line integrals Evaluate the line integral CFdr for the following vector fields F and... Problem 27RE: Evaluating line integrals Evaluate the line integral CFdr for the following vector fields F and... Problem 28RE: Radial fields in R2 are conservative Prove that the radial field F=r|r|p, where r = x, y and p is a... Problem 29RE: Greens Theorem for line integrals Use either form of Greens Theorem to evaluate the following line... Problem 30RE: Greens Theorem for line integrals Use either form of Greens Theorem to evaluate the following line... Problem 31RE: Greens Theorem for line integrals Use either form of Greens Theorem to evaluate the following line... Problem 32RE: Greens Theorem for line integrals Use either form of Greens Theorem to evaluate the following line... Problem 33RE: Areas of plane regions Find the area of the following regions using a line integral. 33.The region... Problem 34RE: Areas of plane regions Find the area of the following regions using a line integral. 34.The region... Problem 35RE: Circulation and flux Consider the following vector fields. a.Compute the circulation on the boundary... Problem 36RE: Circulation and flux Consider the following vector fields. a.Compute the circulation on the boundary... Problem 37RE: Parameters Let F = ax + by, cx + dy, where a, b, c, and d are constants. a.For what values of a, b,... Problem 38RE: Divergence and curl Compute the divergence and curl of the following vector fields. State whether... Problem 39RE: Divergence and curl Compute the divergence and curl of the following vector fields. State whether... Problem 40RE: Divergence and curl Compute the divergence and curl of the following vector fields. State whether... Problem 41RE: Divergence and curl Compute the divergence and curl of the following vector fields. State whether... Problem 42RE: Identities Prove that (1|r|4)=4r|r|6 and use the result to prove that (1|r|4)=12|r|6. Problem 43RE Problem 44RE: Paddle wheel in a vector field Let F = 0, 2x, 0 and let n be a unit vector aligned with the axis of... Problem 45RE: Surface areas Use a surface integral to find the area of the following surfaces. 45.The hemisphere... Problem 46RE: Surface areas Use a surface integral to find the area of the following surfaces. 46.The frustum of... Problem 47RE: Surface areas Use a surface integral to find the area of the following surfaces. 47.The plane z = 6 ... Problem 48RE: Surface areas Use a surface integral to find the area of the following surfaces. 48.The surface... Problem 49RE: Surface integrals Evaluate the following surface integrals. 49.S(1+yz)dS; S is the plane x + y + z =... Problem 50RE: Surface integrals Evaluate the following surface integrals. 50.S0,y,zndS; S is the curved surface of... Problem 51RE: Surface integrals Evaluate the following surface integrals. 51.S(xy+z)dS; S is the entire surface... Problem 52RE: Flux integrals Find the flux of the following vector fields across the given surface. Assume the... Problem 53RE: Flux integrals Find the flux of the following vector fields across the given surface. Assume the... Problem 54RE: Three methods Find the surface area of the paraboloid z = x2 + y2, for 0 z 4, in three ways. a.Use... Problem 55RE: Flux across hemispheres and paraboloids Let S be the hemisphere x2 + y2 + z2 = a2, for z 0, and let... Problem 56RE: Surface area of an ellipsoid Consider the ellipsoid x2/a2 + y2/b2 + z2/c2 = 1, where a, b, and c are... Problem 57RE: Stokes Theorem for line integrals Evaluate the line integral CFdr using Stokes Theorem. Assume C has... Problem 58RE: Stokes Theorem for line integrals Evaluate the line integral CFdr using Stokes Theorem. Assume C has... Problem 59RE: Stokes Theorem for surface integrals Use Stokes Theorem to evaluate the surface integral S(F)ndS.... Problem 60RE: Stokes Theorem for surface integrals Use Stokes Theorem to evaluate the surface integral S(F)ndS.... Problem 61RE: Conservative fields Use Stokes Theorem to find the circulation of the vector field F = (10 x2+ y2 +... Problem 62RE: Computing fluxes Use the Divergence Theorem to compute the outward flux of the following vector... Problem 63RE: Computing fluxes Use the Divergence Theorem to compute the outward flux of the following vector... Problem 64RE: Computing fluxes Use the Divergence Theorem to compute the outward flux of the following vector... Problem 65RE: General regions Use the Divergence Theorem to compute the outward flux of the following vector... Problem 66RE: General regions Use the Divergence Theorem to compute the outward flux of the following vector... Problem 67RE: Flux integrals Compute the outward flux of the field F = x2 + x sin y, y2 + 2 cos y, z2 + z sin y... Problem 68RE: Stokes Theorem on a compound surface Consider the surface S consisting of the quarter-sphere x2 + y2... format_list_bulleted
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning