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2. (25 points) Find the average value of f(x,y) = x + y over the first...
1. Find the integral of the function f(x, y, z)xy+2 z over the region enclosed by the planex +y+z...
please answer question 3.
1. Find the integral of the function f(x, y, z)xy+2 z over the region enclosed by the planex +y+z 2 2. Find the volume and center of gravity for the solid in the first octant (x 20, y 20, z20) bounded by 3. Find the center of mass for the solid hemisphere centered at the origin with radius a if the density and the coordinate planes z0,y 0, and x0 the parabolic ellipsoid Z-4-r-y. function is...
Problem 5. Find saddle points of f(x,y)y sin(a/3). 82+88y6 a local Problem 6. At what point is the function f(x, y) minimum? Problem 7. Use Lagrange multipliers to find the maximum and the minimu...
Problem 5. Find saddle points of f(x,y)y sin(a/3). 82+88y6 a local Problem 6. At what point is the function f(x, y) minimum? Problem 7. Use Lagrange multipliers to find the maximum and the minimum of f(x, y) -yz on the sphere centered at the origin and of radius 3 in R3
Problem 5. Find saddle points of f(x,y)y sin(a/3). 82+88y6 a local Problem 6. At what point is the function f(x, y) minimum? Problem 7. Use Lagrange multipliers to find...
Find the average value of f(x, y) over the region Rwhere A is the area of...
Find the average value of f(x, y) over the region Rwhere A is the area of R in the following equation. Average value - Ā J 1(x,y) dA f(x,y) = xy R: rectangle with vertices (0, 0), (7,0), (1, 2), (0, 2) Enter a number Submit Answer Practice Another Version
2. Find the average value of the function f(x,y) y 2. (Sketch the region.) 1/, y xy over the region bounded by y x, and 2. Find the average value of the function f(x,y) y 2. (Sketch the region.)...
2. Find the average value of the function f(x,y) y 2. (Sketch the region.) 1/, y xy over the region bounded by y x, and
2. Find the average value of the function f(x,y) y 2. (Sketch the region.) 1/, y xy over the region bounded by y x, and
13. (5 points) Reverse the order of integration for the following iterated integral. You do not...
13. (5 points) Reverse the order of integration for the following iterated integral. You do not have to integrate. cos y dy dx 14. (5 points) Integrate the function g(r,0) = p sin over the sector of a disc in the first quadrant bounded by the circle r² + y2 = 1, the circle r² + y2 = 4, the line y = rV3, and the r-axis. 15. (5 points) Convert the following iterated integral from Cartesian to polar. You...
F(x,y) =<2xy,x^2+y^2> the part of the unit circle in the first quadrant oriented counter clockwise 37. F(x, y...
F(x,y) =<2xy,x^2+y^2> the part of the unit circle in the
first quadrant oriented counter clockwise
37. F(x, y) = (2.xy, x2+y2), quadrant oriented counterclockwise the part of the unit circle in the first
37. F(x, y) = (2.xy, x2+y2), quadrant oriented counterclockwise the part of the unit circle in the first
3. Suppose f(x,y,z) - sin2(x) - 2 sin(x)+y'-4yz+52-6z. Find the minimum value of this function- you must find the point at which the minimum occurs and "prove" that the function really ha...
3. Suppose f(x,y,z) - sin2(x) - 2 sin(x)+y'-4yz+52-6z. Find the minimum value of this function- you must find the point at which the minimum occurs and "prove" that the function really has a mini- mum there. Does the function have a maximum? If we restrict the variables to the ball of radius 1, centered at the origin, does the function have a maximum on that set? (You don't have to try to find the maximum but you should try to...
(10 points) First, determine the quadrant for 2; then find x, y, and r; and finally,...
(10 points) First, determine the quadrant for 2; then find x, y, and r; and finally, give all six trigonometric ratios for a given the following information: csc(0) = 1 and cos(0) < 0 e lives in quadrant • X= • y = 1. sin(O) = 2. cos(0) = 3. tan(O) = 4. sec(0) = 5. csc(0) = 6. cot(0) =
Find the average value, I^bar, of the function f(x, y) = 7(x + y)In x over...
Find the average value, I^bar, of the function f(x, y) = 7(x + y)In x over the rectangle A = {(x, y): 1 graterthanequal x graterthanequal 5, 0 graterthanequal y graterthanequal 5}.I^bar = 7 (5 In 5 - 4) I^bar= 7(25/4 ln 5 + 4) I^bar = 7(4/25 in 5 - 4) I^bar = 7 (25/In 5 - 4) I^bar = 7 (25/4 In 5 - 8)
A B C Parametrize, but do not evaluate, //f(x, y, z) ds, where f(x, y, z) 2y22 and S is the part , where J(,y,) 3...
A
B
C
Parametrize, but do not evaluate, //f(x, y, z) ds, where f(x, y, z) 2y22 and S is the part , where J(,y,) 3 3 and 0 Sys4 of the graph of z2 over the rectangle -2 s . Parametrize, but do not evaluate, F.n ds, where F (,-,z) and S is the sphere of radius 2 centered at the origin. Calculate JJs xyz dS where S is the part of the cone parametrized by r(u, u) (ucos...
please answer question 3.
1. Find the integral of the function f(x, y, z)xy+2 z over the region enclosed by the planex +y+z 2 2. Find the volume and center of gravity for the solid in the first octant (x 20, y 20, z20) bounded by 3. Find the center of mass for the solid hemisphere centered at the origin with radius a if the density and the coordinate planes z0,y 0, and x0 the parabolic ellipsoid Z-4-r-y. function is...
Problem 5. Find saddle points of f(x,y)y sin(a/3). 82+88y6 a local Problem 6. At what point is the function f(x, y) minimum? Problem 7. Use Lagrange multipliers to find the maximum and the minimum of f(x, y) -yz on the sphere centered at the origin and of radius 3 in R3
Problem 5. Find saddle points of f(x,y)y sin(a/3). 82+88y6 a local Problem 6. At what point is the function f(x, y) minimum? Problem 7. Use Lagrange multipliers to find...
Find the average value of f(x, y) over the region Rwhere A is the area of R in the following equation. Average value - Ā J 1(x,y) dA f(x,y) = xy R: rectangle with vertices (0, 0), (7,0), (1, 2), (0, 2) Enter a number Submit Answer Practice Another Version
2. Find the average value of the function f(x,y) y 2. (Sketch the region.) 1/, y xy over the region bounded by y x, and
2. Find the average value of the function f(x,y) y 2. (Sketch the region.) 1/, y xy over the region bounded by y x, and
13. (5 points) Reverse the order of integration for the following iterated integral. You do not have to integrate. cos y dy dx 14. (5 points) Integrate the function g(r,0) = p sin over the sector of a disc in the first quadrant bounded by the circle r² + y2 = 1, the circle r² + y2 = 4, the line y = rV3, and the r-axis. 15. (5 points) Convert the following iterated integral from Cartesian to polar. You...
F(x,y) =<2xy,x^2+y^2> the part of the unit circle in the
first quadrant oriented counter clockwise
37. F(x, y) = (2.xy, x2+y2), quadrant oriented counterclockwise the part of the unit circle in the first
37. F(x, y) = (2.xy, x2+y2), quadrant oriented counterclockwise the part of the unit circle in the first
3. Suppose f(x,y,z) - sin2(x) - 2 sin(x)+y'-4yz+52-6z. Find the minimum value of this function- you must find the point at which the minimum occurs and "prove" that the function really has a mini- mum there. Does the function have a maximum? If we restrict the variables to the ball of radius 1, centered at the origin, does the function have a maximum on that set? (You don't have to try to find the maximum but you should try to...
(10 points) First, determine the quadrant for 2; then find x, y, and r; and finally, give all six trigonometric ratios for a given the following information: csc(0) = 1 and cos(0) < 0 e lives in quadrant • X= • y = 1. sin(O) = 2. cos(0) = 3. tan(O) = 4. sec(0) = 5. csc(0) = 6. cot(0) =
Find the average value, I^bar, of the function f(x, y) = 7(x + y)In x over the rectangle A = {(x, y): 1 graterthanequal x graterthanequal 5, 0 graterthanequal y graterthanequal 5}.I^bar = 7 (5 In 5 - 4) I^bar= 7(25/4 ln 5 + 4) I^bar = 7(4/25 in 5 - 4) I^bar = 7 (25/In 5 - 4) I^bar = 7 (25/4 In 5 - 8)
A
B
C
Parametrize, but do not evaluate, //f(x, y, z) ds, where f(x, y, z) 2y22 and S is the part , where J(,y,) 3 3 and 0 Sys4 of the graph of z2 over the rectangle -2 s . Parametrize, but do not evaluate, F.n ds, where F (,-,z) and S is the sphere of radius 2 centered at the origin. Calculate JJs xyz dS where S is the part of the cone parametrized by r(u, u) (ucos...
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