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6 Let V be the olid bourded from belou LT y nyz2 and loounded om abve...
(7) Let 0 < a <b< c< d for a, b,c,d ER. Consider the set S={(u, v)|0 < u < 1, 0 < v < 1} and lt D be the region in the r-y plance tht is thegof S uer the variable transformati...
(7) Let 0 < a <b< c< d for a, b,c,d ER. Consider the set S={(u, v)|0 < u < 1, 0 < v < 1} and lt D be the region in the r-y plance tht is thegof S uer the variable transformation ェ=au + bu, y=cu+du. ) Sketch D in the r-y plane for the case ad -be (a) Sketch D in the r-y plane for the case ad - be0 (c) Calculate the area of D. Show...
Let A-g's, u, v, w, x, y, z), B {q, s, y, z,C-{v, w, x, y,...
Let A-g's, u, v, w, x, y, z), B {q, s, y, z,C-{v, w, x, y, z), and D-6. Specify the following set. 9) Cu B 10) An B
6-Let F(x, y,z) = yi - xj+zx°y?k. Evaluate (V x F) dS where S is the surfacex2232 = 1, z < 0 oriented by the upward-...
6-Let F(x, y,z) = yi - xj+zx°y?k. Evaluate (V x F) dS where S is the surfacex2232 = 1, z < 0 oriented by the upward- pointing unit normal.
6-Let F(x, y,z) = yi - xj+zx°y?k. Evaluate (V x F) dS where S is the surfacex2232 = 1, z
(c) Let F be the vector field on R given by F(x, y, z) = (2x...
(c) Let F be the vector field on R given by F(x, y, z) = (2x +3y, z, 3y + z). (i) Calculate the divergence of F and the curl of F (ii) Let V be the region in IR enclosed by the plane I +2y +z S denote the closed surface that is the boundary of this region V. Sketch a picture of V and S. Then, using the Divergence Theorem, or otherwise, calculate 3 and the XY, YZ...
Please write neatly! 22. Let S denote the plane 2x +y+ 3z = 6 in the...
Please write neatly!
22. Let S denote the plane 2x +y+ 3z = 6 in the first octant with the upward normal, and C denote its triangular boundary. Use Stokes' Theorem to evaluate the line integral F dr where F = <2z - x, x +y +z, 2y-x>.
22. Let S denote the plane 2x +y+ 3z = 6 in the first octant with the upward normal, and C denote its triangular boundary. Use Stokes' Theorem to evaluate the line...
answer all parts, please! (5) Consider the closed volume V contained by the cylinder r2+2-4 and the planes y =-2 and r +y-3. Let the surface S be the boundary of this region. Note that this boundary...
answer all parts, please!
(5) Consider the closed volume V contained by the cylinder r2+2-4 and the planes y =-2 and r +y-3. Let the surface S be the boundary of this region. Note that this boundary consists of three smooth pieces. (a) Clearly sketch and label S. (You may use GeoGebra for this.) (b) In complete sentences, verbally describe what this surface looks like. (c) Find a parametric representation for each of the three parts of the boundary S...
4. Let f(x, y, z) = rytan'() + z sin(xy), < = wy=v²v, z = "....
4. Let f(x, y, z) = rytan'() + z sin(xy), < = wy=v²v, z = ". Find fu and , using the chain rule.
1. (5 pts.) True oR FALSE: (a) Let R denote a plane region, and (u, v) - (u(x, y), v(x, y)) be a ...
1. (5 pts.) True oR FALSE: (a) Let R denote a plane region, and (u, v) - (u(x, y), v(x, y)) be a different set of coordinates for the Cartesian plane. Then for any function F(u, v) F(u, v)dudv-F(u(x, y), v(x, y))drdy (b) Let R denote a plane region, and (u,v) (u(x,y),o(x,y)) be a different set of coordinates for the Cartesian plane. Then dudv (c) Let R denote a square of sidelength 2 defined by the inequalities r S1, ly...
Let F = <z, 0, y> and let S be the oriented surface parametrized by G(u, v) = (u2 − v, u, v2) for 0 ≤ u ≤ 6, −1 ≤ v ≤ 4. Calculate the normal component of F to the surface at P = (24, 5, 1) = G(...
Let F = <z, 0, y> and let S be the oriented surface parametrized by G(u, v) = (u2 − v, u, v2) for 0 ≤ u ≤ 6, −1 ≤ v ≤ 4. Calculate the normal component of F to the surface at P = (24, 5, 1) = G(5, 1).
V76 3k and S be the rectangular region with the orientation shown below. Let +6 (0,0,4)...
V76 3k and S be the rectangular region with the orientation shown below. Let +6 (0,0,4) (2,0,4) (0,2,0) (2, 2,0) Find a normal vector to the plane (in the upward direction). -8j 4k n V 80 Find the area vector. (0, — 8, — 4) | х A (2 5 -(2 5 2 2 Flux = 5 6j and S be a disk of radius 4 on the plane z = 10 - x - y oriented away from the...
(7) Let 0 < a <b< c< d for a, b,c,d ER. Consider the set S={(u, v)|0 < u < 1, 0 < v < 1} and lt D be the region in the r-y plance tht is thegof S uer the variable transformation ェ=au + bu, y=cu+du. ) Sketch D in the r-y plane for the case ad -be (a) Sketch D in the r-y plane for the case ad - be0 (c) Calculate the area of D. Show...
Let A-g's, u, v, w, x, y, z), B {q, s, y, z,C-{v, w, x, y, z), and D-6. Specify the following set. 9) Cu B 10) An B
6-Let F(x, y,z) = yi - xj+zx°y?k. Evaluate (V x F) dS where S is the surfacex2232 = 1, z < 0 oriented by the upward- pointing unit normal.
6-Let F(x, y,z) = yi - xj+zx°y?k. Evaluate (V x F) dS where S is the surfacex2232 = 1, z
(c) Let F be the vector field on R given by F(x, y, z) = (2x +3y, z, 3y + z). (i) Calculate the divergence of F and the curl of F (ii) Let V be the region in IR enclosed by the plane I +2y +z S denote the closed surface that is the boundary of this region V. Sketch a picture of V and S. Then, using the Divergence Theorem, or otherwise, calculate 3 and the XY, YZ...
Please write neatly!
22. Let S denote the plane 2x +y+ 3z = 6 in the first octant with the upward normal, and C denote its triangular boundary. Use Stokes' Theorem to evaluate the line integral F dr where F = <2z - x, x +y +z, 2y-x>.
22. Let S denote the plane 2x +y+ 3z = 6 in the first octant with the upward normal, and C denote its triangular boundary. Use Stokes' Theorem to evaluate the line...
answer all parts, please!
(5) Consider the closed volume V contained by the cylinder r2+2-4 and the planes y =-2 and r +y-3. Let the surface S be the boundary of this region. Note that this boundary consists of three smooth pieces. (a) Clearly sketch and label S. (You may use GeoGebra for this.) (b) In complete sentences, verbally describe what this surface looks like. (c) Find a parametric representation for each of the three parts of the boundary S...
4. Let f(x, y, z) = rytan'() + z sin(xy), < = wy=v²v, z = ". Find fu and , using the chain rule.
1. (5 pts.) True oR FALSE: (a) Let R denote a plane region, and (u, v) - (u(x, y), v(x, y)) be a different set of coordinates for the Cartesian plane. Then for any function F(u, v) F(u, v)dudv-F(u(x, y), v(x, y))drdy (b) Let R denote a plane region, and (u,v) (u(x,y),o(x,y)) be a different set of coordinates for the Cartesian plane. Then dudv (c) Let R denote a square of sidelength 2 defined by the inequalities r S1, ly...
V76 3k and S be the rectangular region with the orientation shown below. Let +6 (0,0,4) (2,0,4) (0,2,0) (2, 2,0) Find a normal vector to the plane (in the upward direction). -8j 4k n V 80 Find the area vector. (0, — 8, — 4) | х A (2 5 -(2 5 2 2 Flux = 5 6j and S be a disk of radius 4 on the plane z = 10 - x - y oriented away from the...
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