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Consider the vector field F(x, y, z) = (z arctan(y2), 22 In(22 +1), 32) Let the...
Consider the vector field F(x, y, z) = (z arctan(y2), 22 In(22 +1), 32) Let the surface S be the part of the sphere x2 + y2 + x2 = 4 that lies above the plane 2=1 and be oriented downwards. (a) Find the divergence of F. (b) Compute the flux integral SS. F . ñ ds.
1) Assume that the joint cumulative distribution of (X,Y) is x F(x, y) A(B+ arctan(C+arctan Find...
1) Assume that the joint cumulative distribution of (X,Y) is x F(x, y) A(B+ arctan(C+arctan Find (1) the efficiency of A B C (2) the joint probability density function of (X,Y). (3) determine the independence of X and Y. (4) E(X)
1) Assume that the joint cumulative distribution of (X,Y) is x F(x, y) A(B+ arctan(C+arctan Find (1) the efficiency of A B C (2) the joint probability density function of (X,Y). (3) determine the independence of X and Y....
please answer both of them and show all the steps , (b) Find or show the limit does not exist:linm (x, y) → (0,0) x2 + y2 8, (b) Show that the following limit does not exist 2 lim (x, y) → (0,0) x...
please answer both of them and show all the steps
, (b) Find or show the limit does not exist:linm (x, y) → (0,0) x2 + y2 8, (b) Show that the following limit does not exist 2 lim (x, y) → (0,0) x2 + y2
, (b) Find or show the limit does not exist:linm (x, y) → (0,0) x2 + y2 8, (b) Show that the following limit does not exist 2 lim (x, y) → (0,0) x2...
1 Use the Divergence Theorem to compute the flux of the field y 5yz, arctan X...
1 Use the Divergence Theorem to compute the flux of the field y 5yz, arctan X COS s(y2)) out of the region E that lies between the spheres (x2 + z2 x2 + z x² + y² + 2² 25 and x2 + y2 + z 81 in the first octant.
2. Find the slope of the tangent line to f(x, y) 6-x2 + xy - y2...
2. Find the slope of the tangent line to f(x, y) 6-x2 + xy - y2 at (4, 2), toward the point (7, 1). Then find the maximum slope and its direction
2. Find the slope of the tangent line to f(x, y) 6-x2 + xy - y2 at (4, 2), toward the point (7, 1). Then find the maximum slope and its direction
2. a) Find a potential of the vector field f(x, y) = (a2 +2xy - y2,...
2. a) Find a potential of the vector field f(x, y) = (a2 +2xy - y2, a2 - 2ry - y2) b) Show that the vector field (e" (sin ry + ycos xy) +2x - 2z, xe" cos ry2y, 1 - 2x) is conservative.
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29 8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42...
8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29
8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29
1. Find the absolute maximum and minimum values of f(r,y) = x2+y2+5y on the disc {(x,...
1. Find the absolute maximum and minimum values of f(r,y) = x2+y2+5y on the disc {(x, y) | x2+y2 < 4}, and identify the points where these values are attained 2. Find the absolute maximum and minimum values of f(x, y) = x3 - 3x - y* + 12y on the closed region bounded by the quadrilateral with vertices at (0,0), (2,2), (2,3), (0,3), and identify the points where these values are attained. 3. A rectangular box is to have...
5 Use the Divergence theorem to find the outward flux. a. F(a, y,z)-(6x2+ + 2xy, 2y + xz, 4x2y); ...
5 Use the Divergence theorem to find the outward flux. a. F(a, y,z)-(6x2+ + 2xy, 2y + xz, 4x2y); G: The solid cut from the first octant by the cylinder x2+y - 4 and the plane 3. (In(x2+Уг),-2z arctan(y/x), z (x2 +y2); G:The solid between the b. F(r, y, z) Vx + y*); G: The solid between the cylinders x2 + y.2 1 and x2+ y2 2, -1szs4. c Fxy)-(2xy', 2x'y, -): G: The solid bounded by the cylinder x?1...
Consider the vector field F(x, y, z) = (z arctan(y2), 22 In(22 +1), 32) Let the surface S be the part of the sphere x2 + y2 + x2 = 4 that lies above the plane 2=1 and be oriented downwards. (a) Find the divergence of F. (b) Compute the flux integral SS. F . ñ ds.
1) Assume that the joint cumulative distribution of (X,Y) is x F(x, y) A(B+ arctan(C+arctan Find (1) the efficiency of A B C (2) the joint probability density function of (X,Y). (3) determine the independence of X and Y. (4) E(X)
1) Assume that the joint cumulative distribution of (X,Y) is x F(x, y) A(B+ arctan(C+arctan Find (1) the efficiency of A B C (2) the joint probability density function of (X,Y). (3) determine the independence of X and Y....
please answer both of them and show all the steps
, (b) Find or show the limit does not exist:linm (x, y) → (0,0) x2 + y2 8, (b) Show that the following limit does not exist 2 lim (x, y) → (0,0) x2 + y2
, (b) Find or show the limit does not exist:linm (x, y) → (0,0) x2 + y2 8, (b) Show that the following limit does not exist 2 lim (x, y) → (0,0) x2...
1 Use the Divergence Theorem to compute the flux of the field y 5yz, arctan X COS s(y2)) out of the region E that lies between the spheres (x2 + z2 x2 + z x² + y² + 2² 25 and x2 + y2 + z 81 in the first octant.
2. Find the slope of the tangent line to f(x, y) 6-x2 + xy - y2 at (4, 2), toward the point (7, 1). Then find the maximum slope and its direction
2. Find the slope of the tangent line to f(x, y) 6-x2 + xy - y2 at (4, 2), toward the point (7, 1). Then find the maximum slope and its direction
2. a) Find a potential of the vector field f(x, y) = (a2 +2xy - y2, a2 - 2ry - y2) b) Show that the vector field (e" (sin ry + ycos xy) +2x - 2z, xe" cos ry2y, 1 - 2x) is conservative.
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29
8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29
1. Find the absolute maximum and minimum values of f(r,y) = x2+y2+5y on the disc {(x, y) | x2+y2 < 4}, and identify the points where these values are attained 2. Find the absolute maximum and minimum values of f(x, y) = x3 - 3x - y* + 12y on the closed region bounded by the quadrilateral with vertices at (0,0), (2,2), (2,3), (0,3), and identify the points where these values are attained. 3. A rectangular box is to have...
5 Use the Divergence theorem to find the outward flux. a. F(a, y,z)-(6x2+ + 2xy, 2y + xz, 4x2y); G: The solid cut from the first octant by the cylinder x2+y - 4 and the plane 3. (In(x2+Уг),-2z arctan(y/x), z (x2 +y2); G:The solid between the b. F(r, y, z) Vx + y*); G: The solid between the cylinders x2 + y.2 1 and x2+ y2 2, -1szs4. c Fxy)-(2xy', 2x'y, -): G: The solid bounded by the cylinder x?1...
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