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Roblem . Compute the areas of the following surfaces. (a) The part of the paraboloid 2 2 that lie...
Compute the following surface areas: (a) the surface area of that part of the plane z...
Compute the following surface areas: (a) the surface area of that part of the plane z = Ar + By C which lies inside the y2 elliptical cylinder 1. (b) the surface area of that part of the cylinder r2 +y2 the sphere 2 y 2 0 which lies inside 2ar 4a2. (Notice the symmetry)
Parameterize the following surfaces in R3. Describe if the surface is open or closed. If the surf...
Parameterize the following surfaces in R3. Describe
if the surface is open or closed. If the surface is open, give a
parameterization of its boundary,
6. Parametrize the following surfaces in R3. Describe if the surface is open or closed. If the surface is open, give a parametrization of its boundary (positively oriented). (a) The part of the plane z - 2y 3 inside the cylinder 2 y16 (b) The sphere of radiuscentered at the origin. (c) The part of...
Let S1 be the part of the paraboloid z = 1 − x ^2 − y...
Let S1 be the part of the paraboloid z = 1 − x ^2 − y ^2 that lies above the plane z = 0. Let S2 be the part of the cone z = √ x ^2 + y ^2 + 2(sqrt till y^2) that lies inside of the cylinder x ^2 + y^ 2 = 1. Let S3 be the part of the cylinder x ^2 + y ^2 = 1 that lies between these surfaces. If S...
2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the pa...
2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the paraboloid z-x2 + y2. Hints: * Complete the square for ×2 + y2 + Z2-42+ (it is a sphere with center (0, 0,) Find the intersection to determine the region of integration
2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the paraboloid z-x2 + y2....
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2. 2. (20 pts) Find the surface area of that part of the sphere x2 + y2 +...
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.
Find the area of the following surfaces. a) The part of the plane 3z + 2y +z 6 that lies in the f...
Solve c and d Please.
Find the area of the following surfaces. a) The part of the plane 3z + 2y +z 6 that lies in the first octant. b) The part of the cone zVy that lies between the plane y z and the cylinder y-x c) The surface with vector equation r(u, u) = (u . cos(v), u . sin(v), u) , where 0 u 1, 0 v S T. d) The portion of the unit sphere that...
ASAP please 1) Compute the surface area of the surface S, which is the part of the sphere x2 + y2 + Z2-4, and that lies between the planes z 0 and z 1. Extra Credit: Does anything strike you as od...
ASAP please
1) Compute the surface area of the surface S, which is the part of the sphere x2 + y2 + Z2-4, and that lies between the planes z 0 and z 1. Extra Credit: Does anything strike you as odd about this answer?]
1) Compute the surface area of the surface S, which is the part of the sphere x2 + y2 + Z2-4, and that lies between the planes z 0 and z 1. Extra Credit: Does...
Let S be part of the paraboloid ~ = x2 + y2 that lies under the plane ž Evaluate the surface inte...
Let S be part of the paraboloid \(z=x^{2}+y^{2}\) that lies under the plane \(z=4\). Evaluate the surface integral \(\iint_{S} z d S\).
Part 1 Part 2. Consider the equipotential surfaces in the picture. The equipotential lines are separated...
Part 1
Part 2.
Consider the equipotential surfaces in the picture. The equipotential lines are separated by 1 cm 300 V -+ +- -200 V -100 V What is the magnitude of the average electric field between points A and C? The maximum charge that can be stored on a conducting sphere is determined by the electric field required the ionize the material surrounding it. Consider a uniform conducting sphere in air. Air ionizes when the electric field at the...
Find a parametrization for each of the following surfaces. [Note: There are many correct answers!] Show...
Find a parametrization for each of the following surfaces. [Note: There are many correct answers!] Show how you arrived at your answer. Hint: It is often helpful to construct your parametrization using (a) cylindrical coordinates, (b) spherical coordi- nates, or (c) by using a parametrization such as (:2, y, 2) = (u, v, f(u, v)) for the surface 2= f(, y). (a) The portion of the sphere x² + y2 + z2 = 9 that is above the cone z...
Compute the following surface areas: (a) the surface area of that part of the plane z = Ar + By C which lies inside the y2 elliptical cylinder 1. (b) the surface area of that part of the cylinder r2 +y2 the sphere 2 y 2 0 which lies inside 2ar 4a2. (Notice the symmetry)
Parameterize the following surfaces in R3. Describe
if the surface is open or closed. If the surface is open, give a
parameterization of its boundary,
6. Parametrize the following surfaces in R3. Describe if the surface is open or closed. If the surface is open, give a parametrization of its boundary (positively oriented). (a) The part of the plane z - 2y 3 inside the cylinder 2 y16 (b) The sphere of radiuscentered at the origin. (c) The part of...
2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the paraboloid z-x2 + y2. Hints: * Complete the square for ×2 + y2 + Z2-42+ (it is a sphere with center (0, 0,) Find the intersection to determine the region of integration
2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the paraboloid z-x2 + y2....
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.
Solve c and d Please.
Find the area of the following surfaces. a) The part of the plane 3z + 2y +z 6 that lies in the first octant. b) The part of the cone zVy that lies between the plane y z and the cylinder y-x c) The surface with vector equation r(u, u) = (u . cos(v), u . sin(v), u) , where 0 u 1, 0 v S T. d) The portion of the unit sphere that...
ASAP please
1) Compute the surface area of the surface S, which is the part of the sphere x2 + y2 + Z2-4, and that lies between the planes z 0 and z 1. Extra Credit: Does anything strike you as odd about this answer?]
1) Compute the surface area of the surface S, which is the part of the sphere x2 + y2 + Z2-4, and that lies between the planes z 0 and z 1. Extra Credit: Does...
Part 1
Part 2.
Consider the equipotential surfaces in the picture. The equipotential lines are separated by 1 cm 300 V -+ +- -200 V -100 V What is the magnitude of the average electric field between points A and C? The maximum charge that can be stored on a conducting sphere is determined by the electric field required the ionize the material surrounding it. Consider a uniform conducting sphere in air. Air ionizes when the electric field at the...
Find a parametrization for each of the following surfaces. [Note: There are many correct answers!] Show how you arrived at your answer. Hint: It is often helpful to construct your parametrization using (a) cylindrical coordinates, (b) spherical coordi- nates, or (c) by using a parametrization such as (:2, y, 2) = (u, v, f(u, v)) for the surface 2= f(, y). (a) The portion of the sphere x² + y2 + z2 = 9 that is above the cone z...
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