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EXAMPLE 1 A transformation is defined by the equations x 4²...
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
A region R in the xy-plane is given. Find equations for a transformation T that maps...
A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u- and v- axes. (Let u play the role of r and v the role of θ. Enter your answers as a comma-separated list of equations.) R lies between the circles x2 + y2 = 1 and x2 + y2 = 7 in the first quadrant
A region R in the xy-plane is given. Find equations for a transformation T that maps...
A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u- and v- axes. (Let u play the role of r and v the role of θ. Enter your answers as a comma-separated list of equations.) R lies between the circles x2 + y2 = 1 and x2 + y2 = 7 in the first quadrant
A region R in the xy-plane is given. Find equations for a transformation T that maps...
A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u-and v-axes. (Let u play the role of r and v the role of θ. Enter your answers as a comma-separated list of equations.) R lies between the circles x2 + y2 1 and x2 y2 8 in the first quadrant Need Help? Read ItJ Watch...
(1 point) Consider the transformation T : x = sau - Sov, y = ou +...
(1 point) Consider the transformation T : x = sau - Sov, y = ou + A. Compute the Jacobian: d(xy) d(u,v) = B. The transformation is linear, which implies that it transforms lines into lines. Thus, it transforms the square S :-50 su < 50, -50 SV < 50 into a square T(S) with vertices: T(50, 50) =( T(-50, 50) =( T(-50, -50) =( T(50, -50) =( C. Use the transformation T to evaluate the integral Stor? + y2...
1. Are £i and C2 skew lines? Explain your answer and find the distance between them if they are s...
1. Are £i and C2 skew lines? Explain your answer and find the distance between them if they are skew lines. 3 marks 2. Let S be the region given by S-((z, y) E R: z2 + y2 4,z? + y2-4y2 0,#2 0, y 20} 1 mark (a) Sketch the region S; (b) Consider the change of variables given by u2 , a2 +y-4y. Describe the region S as set in terms of the variables u and v. Call this...
Please fill in all the blanks and show your work. Video Example) Tutorial Online Textbook EXAMPLE...
Please fill in all the blanks and show your
work.
Video Example) Tutorial Online Textbook EXAMPLE 4 Find the volume of the solid that lies under the paraboloid z = 3x2 + 3y2, above the xy-plane, and inside the cylinder x2 + y2 = 8x. SOLUTION The solid lies above the disk D whose boundary circle has equation x2 + y2 = 8x or, after completing the square, (x - 1 x)2 + y2 = 1 In polar coordinates we...
could u please solve them all Thanks :) (15 points) Evaluate the given integral along positively oriented curve 2 and y2 where C is the boundary of the region enclosed by the parabolas y # (Hint: Use...
could u please solve them all Thanks :)
(15 points) Evaluate the given integral along positively oriented curve 2 and y2 where C is the boundary of the region enclosed by the parabolas y # (Hint: Use Green Theorem). (15 points) Let F = (6fpi + (2x3jj + .k be given. (a) Evaluate f F-dr along the plane curve y = 12 fronn (0.0.0) to (2,4,0). b) Evaluate, curl(F), div(F) and div(curl(F))
(15 points) Evaluate the given integral along positively...
Please show all steps and give explanations 4. a. Solve the system и %3D 2х —...
Please show all steps and give
explanations
4. a. Solve the system и %3D 2х — Зу, v = -x + y for x and y in terms of u and v. Then find the value of the Jacobian d(x, y)/ә(и, v). 2х — Зу, v = -x + y of the parallelogram R in the xy-plane with -3, x 0, y x, and y x + 1. Sketch b. Find the image under the transformation boundaries x = the...
Consider the transformation x = v cos :2πu, y =v sin 2πι. (a) Describe the image...
Consider the transformation x = v cos :2πu, y =v sin 2πι. (a) Describe the image S under T of the unit square R = {(u, v) | 0 1,0 << 1 u (b) Find the area of S.
Consider the transformation x = v cos :2πu, y =v sin 2πι. (a) Describe the image S under T of the unit square R = {(u, v) | 0 1,0
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u-and v-axes. (Let u play the role of r and v the role of θ. Enter your answers as a comma-separated list of equations.) R lies between the circles x2 + y2 1 and x2 y2 8 in the first quadrant Need Help? Read ItJ Watch...
(1 point) Consider the transformation T : x = sau - Sov, y = ou + A. Compute the Jacobian: d(xy) d(u,v) = B. The transformation is linear, which implies that it transforms lines into lines. Thus, it transforms the square S :-50 su < 50, -50 SV < 50 into a square T(S) with vertices: T(50, 50) =( T(-50, 50) =( T(-50, -50) =( T(50, -50) =( C. Use the transformation T to evaluate the integral Stor? + y2...
1. Are £i and C2 skew lines? Explain your answer and find the distance between them if they are skew lines. 3 marks 2. Let S be the region given by S-((z, y) E R: z2 + y2 4,z? + y2-4y2 0,#2 0, y 20} 1 mark (a) Sketch the region S; (b) Consider the change of variables given by u2 , a2 +y-4y. Describe the region S as set in terms of the variables u and v. Call this...
Please fill in all the blanks and show your
work.
Video Example) Tutorial Online Textbook EXAMPLE 4 Find the volume of the solid that lies under the paraboloid z = 3x2 + 3y2, above the xy-plane, and inside the cylinder x2 + y2 = 8x. SOLUTION The solid lies above the disk D whose boundary circle has equation x2 + y2 = 8x or, after completing the square, (x - 1 x)2 + y2 = 1 In polar coordinates we...
could u please solve them all Thanks :)
(15 points) Evaluate the given integral along positively oriented curve 2 and y2 where C is the boundary of the region enclosed by the parabolas y # (Hint: Use Green Theorem). (15 points) Let F = (6fpi + (2x3jj + .k be given. (a) Evaluate f F-dr along the plane curve y = 12 fronn (0.0.0) to (2,4,0). b) Evaluate, curl(F), div(F) and div(curl(F))
(15 points) Evaluate the given integral along positively...
Please show all steps and give
explanations
4. a. Solve the system и %3D 2х — Зу, v = -x + y for x and y in terms of u and v. Then find the value of the Jacobian d(x, y)/ә(и, v). 2х — Зу, v = -x + y of the parallelogram R in the xy-plane with -3, x 0, y x, and y x + 1. Sketch b. Find the image under the transformation boundaries x = the...
Consider the transformation x = v cos :2πu, y =v sin 2πι. (a) Describe the image S under T of the unit square R = {(u, v) | 0 1,0 << 1 u (b) Find the area of S.
Consider the transformation x = v cos :2πu, y =v sin 2πι. (a) Describe the image S under T of the unit square R = {(u, v) | 0 1,0
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