1) Graph the region of the xy-plane on which f(x,y) is non-zero
*Please graph so that I can write on paper without drawing in 3-D (The xy plane)
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1) Graph the region of the xy-plane on which f(x,y) is non-zero *Please graph so that I can write...
10. (a) Find the surface area of the portion of the graph of f(x, y)-yx which is above the region in the xy- plane bounded by y x,y 0 and x.(b) Let f(x)-2 (n+3)2 _____ for each x for which the se...
10. (a) Find the surface area of the portion of the graph of f(x, y)-yx which is above the region in the xy- plane bounded by y x,y 0 and x.(b) Let f(x)-2 (n+3)2 _____ for each x for which the series o 5" converges. Write a power series in summation notation for an indefinite integral of f.
10. (a) Find the surface area of the portion of the graph of f(x, y)-yx which is above the region in the...
Find the area of the region in the XY-plane enclosed by y = 3−x and x...
Find the area of the region in the XY-plane enclosed by y = 3−x and x = 3y−y . In doing so, sketch the region (hint: remember that the graph of a quadratic is a parabola), and be sure to show all your work.
Consider z-f(x,y)-1-xy cos(xy) at (2,-1/2) variations in x and y respectively. and let ΔΧ and ây ...
Consider z-f(x,y)-1-xy cos(xy) at (2,-1/2) variations in x and y respectively. and let ΔΧ and ây represent small a) (i) Compute ΔΖ, given that ΔΧ_ 0.028 and Δy_-0.039. 1 1 6DP Az 5DP ii) Write out an expression for dz in terms of x,y and d, dy. dz= 2 (iii) Compute dz assuming dr_Δι and dy_ây dz- 5DP b) Use the equation of the tangent plane to z at (2,-1/2) to approximate Approximate value = 1 5DP
Consider z-f(x,y)-1-xy cos(xy)...
2. Compute the integral of f over S where (a) f(ayz)xy+z.S is the region in the first octant with...
solve parts b,d and f
2. Compute the integral of f over S where (a) f(ayz)xy+z.S is the region in the first octant with xy+ (b) f(xy.z)xxyz, S is the region defined in 2(a) (c) f(x,y.z) x + y2-xz, s is the region bounded by the x'y plane, the plane z (d) f(x,y,z) 2, and the cylinderx2 y z, s is the region in the first octant bounded by r2 + y2 + 2 4 (e) f(xy,z-2, s is the...
(1 point) The region W lies below the surface f(x,y) = 7e-(æ=3)*"-y* and above the disk x2+y2 < 36 in the xy-pla...
(1 point) The region W lies below the surface f(x,y) = 7e-(æ=3)*"-y* and above the disk x2+y2 < 36 in the xy-plane. (a) Think about what the contours of f look like. You may want to using f(x,y) = 1 as an example. Sketch a rough contour diagram on a separate sheet of paper. (b) Write an integral giving the area of the cross-section of W in the plane = 3. d Area = and b where a= (c) Use...
Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0), (6, 2),...
Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0), (6, 2), (4, 4), (2, 2)
Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0),...
3. About Flux: Suppose F-Ji + 2j-k and s is a region on the plane x + y-z-3. Distinguish the scen...
3. About Flux: Suppose F-Ji + 2j-k and s is a region on the plane x + y-z-3. Distinguish the scenario where we can bypass the flux integral by simply computing F. A and the scenario where we have to integrate using the shadow method. Compute the flux. (a) S is a circle of radius 3 on the plane. O F.A Which method is appropriate? Compute the flux: O shadow method. 2 9 on the xy plane. (b) S is...
Determine a region of the xy-plane for which the given differential equation would have a unique...
Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0, y0) in the region. (25 − y2)y' = x2 Choose the right answer and explain a. A unique solution exists in the regions y < −5, −5 < y < 5, and y > 5. b. A unique solution exists in the region y < 5. c. A unique solution exists in the region consisting of...
2. (20 marks) (a) Calculate the surface area of the graph of f(x,y) = x +...
2. (20 marks) (a) Calculate the surface area of the graph of f(x,y) = x + 20y over the region R= {(x,y) e R2:1 < x < 4,2 sy s 2x} in the xy-plane. OV (b) Integrate the function g(x, y, z) = x +y +z over the surface that is described as follows: x = 2u – v, y = v + 2u, z= v – u Here u € [0,20), v € [0,21].
component functions denoted by y(t) ((t), y(t), z(t). The plane curve t) = (x(t), y(t)) represents the projection of γ onto the xy-plane. Assume that γ, is nowhere parallel to (0,0,1), so that γ...
component functions denoted by y(t) ((t), y(t), z(t). The plane curve t) = (x(t), y(t)) represents the projection of γ onto the xy-plane. Assume that γ, is nowhere parallel to (0,0,1), so that γ is regular. Let K and K denote the curvature functions of y and 7 respectively. Let v,v denote the velocity functions of γ and γ respectively. (1) Prove that R 2RV. In particular, at a time t e I for which v(t) lies in the ay-plane,...
10. (a) Find the surface area of the portion of the graph of f(x, y)-yx which is above the region in the xy- plane bounded by y x,y 0 and x.(b) Let f(x)-2 (n+3)2 _____ for each x for which the series o 5" converges. Write a power series in summation notation for an indefinite integral of f.
10. (a) Find the surface area of the portion of the graph of f(x, y)-yx which is above the region in the...
Consider z-f(x,y)-1-xy cos(xy) at (2,-1/2) variations in x and y respectively. and let ΔΧ and ây represent small a) (i) Compute ΔΖ, given that ΔΧ_ 0.028 and Δy_-0.039. 1 1 6DP Az 5DP ii) Write out an expression for dz in terms of x,y and d, dy. dz= 2 (iii) Compute dz assuming dr_Δι and dy_ây dz- 5DP b) Use the equation of the tangent plane to z at (2,-1/2) to approximate Approximate value = 1 5DP
Consider z-f(x,y)-1-xy cos(xy)...
solve parts b,d and f
2. Compute the integral of f over S where (a) f(ayz)xy+z.S is the region in the first octant with xy+ (b) f(xy.z)xxyz, S is the region defined in 2(a) (c) f(x,y.z) x + y2-xz, s is the region bounded by the x'y plane, the plane z (d) f(x,y,z) 2, and the cylinderx2 y z, s is the region in the first octant bounded by r2 + y2 + 2 4 (e) f(xy,z-2, s is the...
(1 point) The region W lies below the surface f(x,y) = 7e-(æ=3)*"-y* and above the disk x2+y2 < 36 in the xy-plane. (a) Think about what the contours of f look like. You may want to using f(x,y) = 1 as an example. Sketch a rough contour diagram on a separate sheet of paper. (b) Write an integral giving the area of the cross-section of W in the plane = 3. d Area = and b where a= (c) Use...
Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0), (6, 2), (4, 4), (2, 2)
Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0),...
3. About Flux: Suppose F-Ji + 2j-k and s is a region on the plane x + y-z-3. Distinguish the scenario where we can bypass the flux integral by simply computing F. A and the scenario where we have to integrate using the shadow method. Compute the flux. (a) S is a circle of radius 3 on the plane. O F.A Which method is appropriate? Compute the flux: O shadow method. 2 9 on the xy plane. (b) S is...
2. (20 marks) (a) Calculate the surface area of the graph of f(x,y) = x + 20y over the region R= {(x,y) e R2:1 < x < 4,2 sy s 2x} in the xy-plane. OV (b) Integrate the function g(x, y, z) = x +y +z over the surface that is described as follows: x = 2u – v, y = v + 2u, z= v – u Here u € [0,20), v € [0,21].
component functions denoted by y(t) ((t), y(t), z(t). The plane curve t) = (x(t), y(t)) represents the projection of γ onto the xy-plane. Assume that γ, is nowhere parallel to (0,0,1), so that γ is regular. Let K and K denote the curvature functions of y and 7 respectively. Let v,v denote the velocity functions of γ and γ respectively. (1) Prove that R 2RV. In particular, at a time t e I for which v(t) lies in the ay-plane,...
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