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ſcos (n =)drdy - 2 sini where D is defined by x+y=1 Calculate the values of...
1. Calculate the surface area of = Vx2 + y2 that lies between the plane (a)...
1. Calculate the surface area of = Vx2 + y2 that lies between the plane (a) that part of the cone yx and the cylinder y = x2 (b) that part of the surface 1 + 3x +2y2 that lies above the triangle with vertices (0,0), (0,1) and (2,1) z= (c) the helicoid (spiral ramp) defined by r(u, v)= u cos vi +usin vj-+ vk, 0u 1,0 < v < T
1. Calculate the surface area of = Vx2 +...
Find the volume beneath z = f(x,y) and above the region described by the rectangle with...
Find the volume beneath z = f(x,y) and above the region described by the rectangle with vertices (0,0), (2,0), (2,3), and (0,3). f(x,y)=4x^2+9y^2 Hint: compute the double integral required to find the volume under f(x,y) using the limits of integration given by the region on the x-y plane.
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) an...
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
true or false is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If...
true or false
is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If a unit vector u makes the angle of π/4 with the gradient ▽f(P), the directional derivative Duf(P) is equal to |Vf(P)I/2. F 12. There is a point on the hyperboloid 2 -y is parallel to the plane...
(b) Evaluate the double integral e(y-2)/(y+2) dA where D is the triangle with vertices (0,0), (2,0)...
(b) Evaluate the double integral e(y-2)/(y+2) dA where D is the triangle with vertices (0,0), (2,0) and (0,2). (Hint: Change variables, let u = y - x and v = y + x.)
16.1 Evaluate [[cz + 3y – x²dS where S is the portion z = 2 –...
16.1
Evaluate [[cz + 3y – x²dS where S is the portion z = 2 – 3y + x2 that lies over the triangle in the xy-plane with vertices (0,0), (2,0), (2, -4).
...HELPPPP....Use Green’s theorem to evaluate Z C (−y + √3 x 2 )dx + (x 3...
...HELPPPP....Use Green’s theorem to evaluate Z C (−y + √3 x 2
)dx + (x 3 − ln (y 2 ))dy where C is the rectangle with vertices
(0, 0), (1, 0), (0, 2), and (1, 2).
4. Use Green's theorem to evaluate vertices (0,0), (1,0), (0, 2), and (1,2). Sc(-y + V 22)dx + (z? – In (y?))dy where C is the rectangle with
1/3 x + y 7. Consider dA where R is the region bounded by the triangle...
1/3 x + y 7. Consider dA where R is the region bounded by the triangle with vertices (0,0), (2,0), V= x+y X-y and (0,-2). The change of variables u=- defines a transformation T(x,y)=(u,v) from the xy-plane 2 to the uv-plane. (a) (10 pts) Write S (in terms of u and v) using set- builder notation, where T:R→S. Use T to help you sketch S in the uv-plane by evaluating T at the vertices. - 1 a(u,v) (b) (4 pts)...
8. Find the surface area of the part of the plane z+y+z4 over the rectangle [0, 1]x[0,2 b) 3 c) 2...
8. Find the surface area of the part of the plane z+y+z4 over the rectangle [0, 1]x[0,2 b) 3 c) 2v3 d) 8 e) 12
8. Find the surface area of the part of the plane z+y+z4 over the rectangle [0, 1]x[0,2 b) 3 c) 2v3 d) 8 e) 12
1. Calculate the surface area of = Vx2 + y2 that lies between the plane (a) that part of the cone yx and the cylinder y = x2 (b) that part of the surface 1 + 3x +2y2 that lies above the triangle with vertices (0,0), (0,1) and (2,1) z= (c) the helicoid (spiral ramp) defined by r(u, v)= u cos vi +usin vj-+ vk, 0u 1,0 < v < T
1. Calculate the surface area of = Vx2 +...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
true or false
is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If a unit vector u makes the angle of π/4 with the gradient ▽f(P), the directional derivative Duf(P) is equal to |Vf(P)I/2. F 12. There is a point on the hyperboloid 2 -y is parallel to the plane...
(b) Evaluate the double integral e(y-2)/(y+2) dA where D is the triangle with vertices (0,0), (2,0) and (0,2). (Hint: Change variables, let u = y - x and v = y + x.)
16.1
Evaluate [[cz + 3y – x²dS where S is the portion z = 2 – 3y + x2 that lies over the triangle in the xy-plane with vertices (0,0), (2,0), (2, -4).
...HELPPPP....Use Green’s theorem to evaluate Z C (−y + √3 x 2
)dx + (x 3 − ln (y 2 ))dy where C is the rectangle with vertices
(0, 0), (1, 0), (0, 2), and (1, 2).
4. Use Green's theorem to evaluate vertices (0,0), (1,0), (0, 2), and (1,2). Sc(-y + V 22)dx + (z? – In (y?))dy where C is the rectangle with
1/3 x + y 7. Consider dA where R is the region bounded by the triangle with vertices (0,0), (2,0), V= x+y X-y and (0,-2). The change of variables u=- defines a transformation T(x,y)=(u,v) from the xy-plane 2 to the uv-plane. (a) (10 pts) Write S (in terms of u and v) using set- builder notation, where T:R→S. Use T to help you sketch S in the uv-plane by evaluating T at the vertices. - 1 a(u,v) (b) (4 pts)...
8. Find the surface area of the part of the plane z+y+z4 over the rectangle [0, 1]x[0,2 b) 3 c) 2v3 d) 8 e) 12
8. Find the surface area of the part of the plane z+y+z4 over the rectangle [0, 1]x[0,2 b) 3 c) 2v3 d) 8 e) 12
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