Homework Answers
Given that
we have to find an approximation to the area of the surface on the hemisphere
x2 + y2 + z2 = 9, z>= 0
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Question 8: 10 Marks The area of the surface described by zf(x,y) for (r,)e R is given by Find an...
8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29 8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42...
8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29
8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29
Find the area of the surface given by z = f(x, y) over the region R....
Find the area of the surface given by z = f(x, y) over the region R. (Hint: Some of the integrals are simpler in polar coordinates.) f(x, y) = x2 + y2, R = {(x, y): 0 = f(x,y) 3}
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be the hemisphere 2 F(x, y,z)-yitj+3z k. Calculate JJs F d...
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be the hemisphere 2 F(x, y,z)-yitj+3z k. Calculate JJs F dS, the flux of F across S
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be...
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...
Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (...
Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (i Determine the level curves for the surface when z on the same diagram in the r-y plane. 1 and 2, Sketch the level curves (i) Determine the cross-sectional curves of the surface in the r-z plane and in the y- plane. Sketch the two cross-sectional curves (iii) Sketch the surface. (b) For the point (r, y)...
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...
z-(x, y)over the region R. 9. Find the area of the surface given by.y)over the region...
z-(x, y)over the region R. 9. Find the area of the surface given by.y)over the region R. f(x, y)--3-4x +2y R: square with vertices (0, 0), (5, 0), (5, 5), (o, 5)
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...
8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29
8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29
Find the area of the surface given by z = f(x, y) over the region R. (Hint: Some of the integrals are simpler in polar coordinates.) f(x, y) = x2 + y2, R = {(x, y): 0 = f(x,y) 3}
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be the hemisphere 2 F(x, y,z)-yitj+3z k. Calculate JJs F dS, the flux of F across S
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be...
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...
Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (i Determine the level curves for the surface when z on the same diagram in the r-y plane. 1 and 2, Sketch the level curves (i) Determine the cross-sectional curves of the surface in the r-z plane and in the y- plane. Sketch the two cross-sectional curves (iii) Sketch the surface. (b) For the point (r, y)...
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...
z-(x, y)over the region R. 9. Find the area of the surface given by.y)over the region R. f(x, y)--3-4x +2y R: square with vertices (0, 0), (5, 0), (5, 5), (o, 5)
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...
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