Homework Answers
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient...
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient of the function f(x, y, z) at the point P,(2,-1,-7). (ii) Find the directional derivative of f(x, y, z) at P,(2,-1,-7) along the direction of the vector ū = 2î+j+2k. (iii) Find the equation of the tangent plane to the surface given below at the point P,(2,-1, -7). 6 :- xcos(ty) + = 0 xy
Find a formula for the distance from the point P{x,y,z) to each of the following planes....
Find a formula for the distance from the point P{x,y,z) to each of the following planes. a. Find the distance from P(x,y,z) to the xy-plane. b. Find the distance from P(x,y,z) to the yz-plane. c. Find the distance from P(x,y,z) to the xz-plane. a. Choose the correct formula for the distance from the point P(x,y,z) to the xy-plane. O A. Iz OB. Mx2 + y2 OC. Vz OD. x² + y² + 2? b. Choose the correct formula for the...
4. Use Stokes' Theorem to evaluate F dr. F(x,y,z)-(3z,4x, 2y); C is the circle x2 +...
4. Use Stokes' Theorem to evaluate F dr. F(x,y,z)-(3z,4x, 2y); C is the circle x2 + y2 4 in the xy-plane with a counterclockwise orientation looking down the positive z-axis. az az F dr-JI, (curl F) n ds and VGy, 1) Hint: use ax' dy
Use the gradient rules to find the gradient of the given function, f(x,y,z) = x+yz y+xz...
Use the gradient rules to find the gradient of the given function, f(x,y,z) = x+yz y+xz Choose the correct answer below. 1 O A. Vf(x,y,z) = -((1-z?)z(z2 - 1).y? - x?) (y + xz)? OB. Vf(x,y,z) = (z(1-z?)y(z? - 1),z2 + x2) (x + yz)? O c. Vf(x,y,z) = (y(1+z2),x(z? + 1).y? - z?) (x + yz)? OD. Vf(x,y,z) = -(y (1-2²), x(2² - 1), y² - x²) (y + xz)2
Find the volume of the region between the planes x +y+3z 3 and 4x+4y Z 12 in the first octant. The volume is (Type an integer or a simplified fraction .) Find the volume of the region between th...
Find the volume of the region between the planes x +y+3z 3 and 4x+4y Z 12 in the first octant. The volume is (Type an integer or a simplified fraction .)
Find the volume of the region between the planes x +y+3z 3 and 4x+4y Z 12 in the first octant. The volume is (Type an integer or a simplified fraction .)
Using stokes theorem (No point otherwise) find the F.dt, F vector=<z,-z,x^2-y^2> and C is the three...
Using stokes theorem (No point otherwise) find the F.dt, F
vector=<z,-z,x^2-y^2> and C is the three lines in which
z=8-4x-2y (plane) cuts the coordinate planes.
Please be detail, thanks.
5. USING STOKES THEOREM (NO POINTS OTHERWISE, FIND FocF, F={z LINES IN WHICH 258-4xby CIMKE COORDINATE PLANES (2, -2, x-x) AND CK THE THR 1 of 1
Using stokes theorem (No point otherwise) find the F.dt, F vector=<z,-z,x^2-y^2> and C is the three...
Using stokes theorem (No point otherwise) find the F.dt, F
vector=<z,-z,x^2-y^2> and C is the three lines in which
z=8-4x-2y (plane) cuts the coordinate planes.
Please be detail, thanks.
5. USING STOKES THEOREM (NO POINTS OTHERWISE, FIND FocF, F={z LINES IN WHICH 258-4xby CIMKE COORDINATE PLANES (2, -2, x-x) AND CK THE THR 1 of 1
8. (12 points) Use the Divergence Theorem to calculate the surface integral [F-dS, where F(x, y,z) (2xyz -3x2 y) i+(3xy-yz) j+(2x2 +32) k, and S is enclosed by the 3z) k, and S is enclosed by the coo...
8. (12 points) Use the Divergence Theorem to calculate the surface integral [F-dS, where F(x, y,z) (2xyz -3x2 y) i+(3xy-yz) j+(2x2 +32) k, and S is enclosed by the 3z) k, and S is enclosed by the coordinate planes and x+y+z = 6
8. (12 points) Use the Divergence Theorem to calculate the surface integral [F-dS, where F(x, y,z) (2xyz -3x2 y) i+(3xy-yz) j+(2x2 +32) k, and S is enclosed by the 3z) k, and S is enclosed by the...
(c) Each equation below specifies a line or a plane in R3. If possible, express the...
(c) Each equation below specifies a line or a plane in R3. If possible, express the specified line or plane as a span. Otherwise, justify why it cannot be expressed as a span. i. 2x-yz=4 ii. х+6у—z%3D 0 iii. x+3z = 0 iv. у %3D1 v. x = 0 and z = 0 vi. 2x -y 2 and z =-1 (d) For lines or planes in question 4c that cannot be expressed as spans, express as a translated span
(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...
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient of the function f(x, y, z) at the point P,(2,-1,-7). (ii) Find the directional derivative of f(x, y, z) at P,(2,-1,-7) along the direction of the vector ū = 2î+j+2k. (iii) Find the equation of the tangent plane to the surface given below at the point P,(2,-1, -7). 6 :- xcos(ty) + = 0 xy
Find a formula for the distance from the point P{x,y,z) to each of the following planes. a. Find the distance from P(x,y,z) to the xy-plane. b. Find the distance from P(x,y,z) to the yz-plane. c. Find the distance from P(x,y,z) to the xz-plane. a. Choose the correct formula for the distance from the point P(x,y,z) to the xy-plane. O A. Iz OB. Mx2 + y2 OC. Vz OD. x² + y² + 2? b. Choose the correct formula for the...
4. Use Stokes' Theorem to evaluate F dr. F(x,y,z)-(3z,4x, 2y); C is the circle x2 + y2 4 in the xy-plane with a counterclockwise orientation looking down the positive z-axis. az az F dr-JI, (curl F) n ds and VGy, 1) Hint: use ax' dy
Use the gradient rules to find the gradient of the given function, f(x,y,z) = x+yz y+xz Choose the correct answer below. 1 O A. Vf(x,y,z) = -((1-z?)z(z2 - 1).y? - x?) (y + xz)? OB. Vf(x,y,z) = (z(1-z?)y(z? - 1),z2 + x2) (x + yz)? O c. Vf(x,y,z) = (y(1+z2),x(z? + 1).y? - z?) (x + yz)? OD. Vf(x,y,z) = -(y (1-2²), x(2² - 1), y² - x²) (y + xz)2
Find the volume of the region between the planes x +y+3z 3 and 4x+4y Z 12 in the first octant. The volume is (Type an integer or a simplified fraction .)
Find the volume of the region between the planes x +y+3z 3 and 4x+4y Z 12 in the first octant. The volume is (Type an integer or a simplified fraction .)
Using stokes theorem (No point otherwise) find the F.dt, F
vector=<z,-z,x^2-y^2> and C is the three lines in which
z=8-4x-2y (plane) cuts the coordinate planes.
Please be detail, thanks.
5. USING STOKES THEOREM (NO POINTS OTHERWISE, FIND FocF, F={z LINES IN WHICH 258-4xby CIMKE COORDINATE PLANES (2, -2, x-x) AND CK THE THR 1 of 1
Using stokes theorem (No point otherwise) find the F.dt, F
vector=<z,-z,x^2-y^2> and C is the three lines in which
z=8-4x-2y (plane) cuts the coordinate planes.
Please be detail, thanks.
5. USING STOKES THEOREM (NO POINTS OTHERWISE, FIND FocF, F={z LINES IN WHICH 258-4xby CIMKE COORDINATE PLANES (2, -2, x-x) AND CK THE THR 1 of 1
8. (12 points) Use the Divergence Theorem to calculate the surface integral [F-dS, where F(x, y,z) (2xyz -3x2 y) i+(3xy-yz) j+(2x2 +32) k, and S is enclosed by the 3z) k, and S is enclosed by the coordinate planes and x+y+z = 6
8. (12 points) Use the Divergence Theorem to calculate the surface integral [F-dS, where F(x, y,z) (2xyz -3x2 y) i+(3xy-yz) j+(2x2 +32) k, and S is enclosed by the 3z) k, and S is enclosed by the...
(c) Each equation below specifies a line or a plane in R3. If possible, express the specified line or plane as a span. Otherwise, justify why it cannot be expressed as a span. i. 2x-yz=4 ii. х+6у—z%3D 0 iii. x+3z = 0 iv. у %3D1 v. x = 0 and z = 0 vi. 2x -y 2 and z =-1 (d) For lines or planes in question 4c that cannot be expressed as spans, express as a translated span
(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...
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