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In Problems 7-14 determine the region(s) of the x-y plane where solutions (i) exist and also...
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...
Use Stokes' Theorem to evaluate. 8. Use Stokes, Theorem to evaluate J, ▽ x ที่ do, where F(x, y, z)-(z2yz,yz2,23ezy and s is part of the sphere x2 + y2 + z-5 that lies above the plane z-1. Also, s...
Use Stokes' Theorem to evaluate.
8. Use Stokes, Theorem to evaluate J, ▽ x ที่ do, where F(x, y, z)-(z2yz,yz2,23ezy and s is part of the sphere x2 + y2 + z-5 that lies above the plane z-1. Also, s is oriented upward.
8. Use Stokes, Theorem to evaluate J, ▽ x ที่ do, where F(x, y, z)-(z2yz,yz2,23ezy and s is part of the sphere x2 + y2 + z-5 that lies above the plane z-1. Also, s is oriented...
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points). f(y) to determine where solutions are i...
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points). f(y) to determine where solutions are increasing / decreasing. Use the sign of y' e) (3 points) Sketch several solution curves in each region determined by the critical poins in the ty-plane
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points)....
(a) Sketch the region in the (x,y) plane where ??,?(?, ?) ≠ 0. (b) Find the...
(a) Sketch the region in the (x,y) plane where ??,?(?, ?) ≠
0.
(b) Find the marginal probability density functions ??(?) and
??(?) of ? and ? respectively.
(c) Are X and Y independent?
(d) Find P(Y>X).
(e) Let y be some real number in the range 0 ≤ y ≤ 1. Find the
conditional probability density function ??|?(?|?).
(f) Find ?[?|? = ?] (where ? is some real number in the range 0
≤ ? ≤ 1).
The joint...
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)...
Determine the following integral where D is the region bounded by x = y, y =...
Determine the following integral where D is the region bounded by x = y, y = 0 and x+y= 2. S S (1 + xy") da = D [3 points]
7. (16pts) Use Stokes, Theorem to find ▽ × F . nd.S where s is the surface of the cube 0 < x < 1, 0Sy, and 0szS 1 with open bottom in the ry plane. F(x, y, z)-<y, -, z > and the normal fi...
7. (16pts) Use Stokes, Theorem to find ▽ × F . nd.S where s is the surface of the cube 0 < x < 1, 0Sy, and 0szS 1 with open bottom in the ry plane. F(x, y, z)-<y, -, z > and the normal field n is oriented so that it points up on the top surface. T, zand
7. (16pts) Use Stokes, Theorem to find ▽ × F . nd.S where s is the surface of the cube...
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...
problems 14 and 15, let R = {(x,y) : x2 + y2 s 2 and y...
problems 14 and 15, let R = {(x,y) : x2 + y2 s 2 and y 2 -x}. Sketch the region of integration for the integral: ll -(X+Y) DA -2 -15 -105051 Compute: e-(x+y) dA and show all work.
(6) Show that F(x, y) = (x+y)i + (**)is conservative. (a) Then find such that S...
(6) Show that F(x, y) = (x+y)i + (**)is conservative. (a) Then find such that S = F (potential function). (5) Use the results in part(a) to cakulae ( F. ds along C which the curve y = a* from (0,0) to (2,16). (2) Use Green's Theorem to evaluate 1. F. ds. F(1,y) =(yº+sin(26))i + (2xy2 + cos y)and C is the unit circle oriented counter clockwise (6) Evaluate the surface integral || 9. ds. F(x,y,z) = xi +++where S...
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...
Use Stokes' Theorem to evaluate.
8. Use Stokes, Theorem to evaluate J, ▽ x ที่ do, where F(x, y, z)-(z2yz,yz2,23ezy and s is part of the sphere x2 + y2 + z-5 that lies above the plane z-1. Also, s is oriented upward.
8. Use Stokes, Theorem to evaluate J, ▽ x ที่ do, where F(x, y, z)-(z2yz,yz2,23ezy and s is part of the sphere x2 + y2 + z-5 that lies above the plane z-1. Also, s is oriented...
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points). f(y) to determine where solutions are increasing / decreasing. Use the sign of y' e) (3 points) Sketch several solution curves in each region determined by the critical poins in the ty-plane
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points)....
(a) Sketch the region in the (x,y) plane where ??,?(?, ?) ≠
0.
(b) Find the marginal probability density functions ??(?) and
??(?) of ? and ? respectively.
(c) Are X and Y independent?
(d) Find P(Y>X).
(e) Let y be some real number in the range 0 ≤ y ≤ 1. Find the
conditional probability density function ??|?(?|?).
(f) Find ?[?|? = ?] (where ? is some real number in the range 0
≤ ? ≤ 1).
The joint...
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)...
Determine the following integral where D is the region bounded by x = y, y = 0 and x+y= 2. S S (1 + xy") da = D [3 points]
7. (16pts) Use Stokes, Theorem to find ▽ × F . nd.S where s is the surface of the cube 0 < x < 1, 0Sy, and 0szS 1 with open bottom in the ry plane. F(x, y, z)-<y, -, z > and the normal field n is oriented so that it points up on the top surface. T, zand
7. (16pts) Use Stokes, Theorem to find ▽ × F . nd.S where s is the surface of the cube...
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...
problems 14 and 15, let R = {(x,y) : x2 + y2 s 2 and y 2 -x}. Sketch the region of integration for the integral: ll -(X+Y) DA -2 -15 -105051 Compute: e-(x+y) dA and show all work.
(6) Show that F(x, y) = (x+y)i + (**)is conservative. (a) Then find such that S = F (potential function). (5) Use the results in part(a) to cakulae ( F. ds along C which the curve y = a* from (0,0) to (2,16). (2) Use Green's Theorem to evaluate 1. F. ds. F(1,y) =(yº+sin(26))i + (2xy2 + cos y)and C is the unit circle oriented counter clockwise (6) Evaluate the surface integral || 9. ds. F(x,y,z) = xi +++where S...
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