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6) The Surface s of the function g(x, y,...
Evaluate the surface integral of the function G over the surface S. 15) G(x, y, z)-x z: S Is the surface of the wedge formed from the coordinate planes and the planes 15) X +z 4 and y 4 A) 128+ 6...
Evaluate the surface integral of the function G over the surface S. 15) G(x, y, z)-x z: S Is the surface of the wedge formed from the coordinate planes and the planes 15) X +z 4 and y 4 A) 128+ 64 320 320
Evaluate the surface integral of the function G over the surface S. 15) G(x, y, z)-x z: S Is the surface of the wedge formed from the coordinate planes and the planes 15) X +z 4...
Please do a step-by-step and clean solution X: 0 1 2 3 4 5 Using the...
Please do a step-by-step and clean solution
X: 0 1 2 3 4 5 Using the table, find the value of y = x^3-20x + 16 polynomial y: 16 -3 -16 -17 0 41 for 0.7 using the Gregory Newton relation. (Hint: use forward finite differences)
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].
Consider the surface given as a graph of the function g(x, y) = x∗y 2 ∗cos(y). The gradient of g ...
Consider the surface given as a graph of the function g(x, y) = x∗y 2 ∗cos(y). The gradient of g represents the direction in which g increases the fastest. Notice that this is the direction in the xy plane corresponding to the steepest slope up the surface, with magnitude equal to the slope in that direction. 1. At the point (2, π), find the gradient, and explain what it means. 2. Use it to construct a vector in the tangent...
Consider the function f (x, y)=6-32 -32 (a) Determine the level curves for the surface when...
Consider the function f (x, y)=6-32 -32 (a) Determine the level curves for the surface when z 0,3, 6. Sketch these three level curves in the ry plane. (b) Determine the cross-sectional curves of the surface in the rz plane and in the yz plane. Sketch these two cross-sectional curves. (c) Sketch the surface z f(x, y) (d) What is the maximal domain and range of f? (e) Evaluate the double integral f(ar, y) da dy
Consider the function f...
V=<x,x,x+y>; Calculate the Stoke's theorem where S is the surface obtained by the intersect...
V=<x,x,x+y>; Calculate the Stoke's theorem where S is the surface obtained by the intersection of a cylinder and a plane. Cylinder of radius R=3, with open upper lid the circle C, x^2+y^2=9. This cylinder has axis the z-axis, with z<=0. The cylinder is cut by plane of equation x + y + z =- 40. This surface looks like a water glass in normal position with its rim the circle C, but slanted (inclined) bottom in the z<0 region The...
Could you do number 4 please. Thanks 1-8 Evaluate the surface integral s. f(x, y, z) ds Vx2ty2 -vr+) 1. f(x, y, z) Z2; ơ is the portion of the cone z between the planes z 1 and z 2 1 2. f(x, y, z)...
Could you do number 4 please. Thanks
1-8 Evaluate the surface integral s. f(x, y, z) ds Vx2ty2 -vr+) 1. f(x, y, z) Z2; ơ is the portion of the cone z between the planes z 1 and z 2 1 2. f(x, y, z) xy; ơ is the portion of the plane x + y + z lying in the first octant. 3. f(x, y, z) x2y; a is the portion of the cylinder x2z2 1 between the planes...
5 and 6 please 5) Given the surface f(x, y, z) = 0 or z =...
5 and 6 please
5) Given the surface f(x, y, z) = 0 or z = f(x,y), find the tangent plane at P. a) z2 – 2x2 – 2y2 = 12 @ P=(1,-1,4) b) f(x,y) = 2x - 3xy3 @ 12,-1) c) f(x,y) = sin(x) @ (3,5) 6) Find an equation of the tangent plane and the equation of the normal line to surface f(x..zb=0 @P x2 + y2 + z2 = 9 P = (2,2,1)
Integrate the given function over the given surface. G(x,y,z) = x over the parabolic cylinder y...
Integrate the given function over the given surface. G(x,y,z) = x over the parabolic cylinder y = x205x< 12,0sz<2 Integrate the function. Sfax.y.z) do=0 (Type an integer or a simplified fraction.)
please show the work for the solution and use surface z = y and then set...
please show the work for the solution and use surface z = y and
then set up G(x,y,z) = z-y. Thanks!
Use Stokes Theorem to evaluate $F F. dr where F(x, y, z) = ryi+yzj+z?k and C is the intersection of the paraboloid z = x² + y² and the plane z = y with a counterclockwise orientation looking down the positive z-axis. HINT: The polar equation r = 2a sin 0, 0 <O< represents a circle with center (0,...
Evaluate the surface integral of the function G over the surface S. 15) G(x, y, z)-x z: S Is the surface of the wedge formed from the coordinate planes and the planes 15) X +z 4 and y 4 A) 128+ 64 320 320
Evaluate the surface integral of the function G over the surface S. 15) G(x, y, z)-x z: S Is the surface of the wedge formed from the coordinate planes and the planes 15) X +z 4...
Please do a step-by-step and clean solution
X: 0 1 2 3 4 5 Using the table, find the value of y = x^3-20x + 16 polynomial y: 16 -3 -16 -17 0 41 for 0.7 using the Gregory Newton relation. (Hint: use forward finite differences)
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].
Consider the function f (x, y)=6-32 -32 (a) Determine the level curves for the surface when z 0,3, 6. Sketch these three level curves in the ry plane. (b) Determine the cross-sectional curves of the surface in the rz plane and in the yz plane. Sketch these two cross-sectional curves. (c) Sketch the surface z f(x, y) (d) What is the maximal domain and range of f? (e) Evaluate the double integral f(ar, y) da dy
Consider the function f...
Could you do number 4 please. Thanks
1-8 Evaluate the surface integral s. f(x, y, z) ds Vx2ty2 -vr+) 1. f(x, y, z) Z2; ơ is the portion of the cone z between the planes z 1 and z 2 1 2. f(x, y, z) xy; ơ is the portion of the plane x + y + z lying in the first octant. 3. f(x, y, z) x2y; a is the portion of the cylinder x2z2 1 between the planes...
5 and 6 please
5) Given the surface f(x, y, z) = 0 or z = f(x,y), find the tangent plane at P. a) z2 – 2x2 – 2y2 = 12 @ P=(1,-1,4) b) f(x,y) = 2x - 3xy3 @ 12,-1) c) f(x,y) = sin(x) @ (3,5) 6) Find an equation of the tangent plane and the equation of the normal line to surface f(x..zb=0 @P x2 + y2 + z2 = 9 P = (2,2,1)
Integrate the given function over the given surface. G(x,y,z) = x over the parabolic cylinder y = x205x< 12,0sz<2 Integrate the function. Sfax.y.z) do=0 (Type an integer or a simplified fraction.)
please show the work for the solution and use surface z = y and
then set up G(x,y,z) = z-y. Thanks!
Use Stokes Theorem to evaluate $F F. dr where F(x, y, z) = ryi+yzj+z?k and C is the intersection of the paraboloid z = x² + y² and the plane z = y with a counterclockwise orientation looking down the positive z-axis. HINT: The polar equation r = 2a sin 0, 0 <O< represents a circle with center (0,...
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