Let S CR be the tetrahedron having vertices (0,0,0), (0,1,1), (1, 2, 3), and (-1,0,1). Let...
Let S CR be the tetrahedron having vertices (0,0,0), (0,1,1), (1,2,3), and (-1,0,1). Let f : R3 +R be the function defined by f(x, y, z) = 1 - 2y + 3z. Using the change of variables theorem, rewrite Is f as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral
Let S CR be the tetrahedron having vertices (0,0,0), (0,1,1), (1,2,3), and (-1,0,1). Let f: R3 → R be the function defined by f(x, y, z) = 1 - 2y + 32. Using the change of variables theorem, rewrite Ss f as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral (8 points).
Don't give the same solution. Let S CR be the tetrahedron having vertices (0,0,0), (0,1,1), (1,2,3), and (-1,0,1). Let f: R3 +R be the function defined by f(x, y, z) = 2 - 2y + 3z. Using the change of variables theorem, rewrite Js f as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral
6. Let S CR be the tetrahedron having vertices (0,0,0), (0, 1, 1), (1, 2, 3), and (-1,0,1). Let f:R3 → R be the function defined by f(x, y, x) = x – 2y + 3z. Using the change of variables theorem, rewrite Ss f as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral (8 points).
Let S ⊆ be the tetrahedron having vertices (0, 0, 0), (0, 1, 1), (1, 2, 3), and (−1, 0, 1). Let f : → be the function defined by f(x, y, x) = x − 2y + 3z. Using the change of variables theorem, rewrite as an integral over a 3-rectangle, then use Fubini’s theorem to evaluate the integral. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image}
1. Given force F-xi 4zj Path 1: (0,0,0) to (0,1,1) Path 2: (0,1,1) to (1,1,0) Path 3: (1,1,0) to (0,0,0) 5yk acts following the path: . Sketch the motion in Cartesian coordinate Write the parametric equation for each path Calculate the total work done by force F which is moving from Path 1 to 3 2. A vector M is defined by M-x2yi xyj and region R corresponds to Sketch the region of R in Cartesian coordinate . Evaluate the...
4. Let F(x, y, z)=(y,x,z2). Let S be the surface of the tetrahedron with the vertices (0,0,0), (2,0,0), (0,2,0), and (0,0,2). Use the divergence theorem to evaluate SS F.dS. (13 points)
(3) Verify the Divergence Theorem for F(x, y, z)-(zy, yz, xz) and the solid tetrahedron with vertices (0,0,0), (1,0,0), (0, 2,0), and (0, 0,1 (3) Verify the Divergence Theorem for F(x, y, z)-(zy, yz, xz) and the solid tetrahedron with vertices (0,0,0), (1,0,0), (0, 2,0), and (0, 0,1
2. Let S be the interior of the triangle with vertices (0,0,0), (1,0,0) and (0,1,0). a) Given F(x, y, z)=(x+1)i +(y+1)] +(2+1)k, calculate the flux of through S without using an integral b) F(x, y, z) = (z+1)7 +(y+1) 7+(x+1)k , set up an iterated integral in dx dy or dy dx to calculate the flux of F through S. You do not need to evaluate your integral
e. 1 Puestion 16 Let E be the solid tetrahedron with vertices (1,1,0), (1,0,4), (0,1,4), (1,1,4). Let D Hot yet answered be the projection of E onto xy-plane. If I dV = / f(x,y) dĄ, then f(x, y) = Marked out of 3.00 Flag question Select one: O a. 3 + 3x + 3y b. 1 + 5x + 5y c. 1 + 6x + 6y d. None of these e. 2 + 2x + 2y O f. 4 +...