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The centroid of a surface o is defined by lo xds area of o lloyds area...
The centroid of a surface o is defined by f= lo xd area of o y...
The centroid of a surface o is defined by f= lo xd area of o y loyds area of o Do zds area of o 1 1 Find the centroid of the portion of the paraboloid z = 3(x2 + y2) below the plane z = 40. Enter the exact answers as improper fractions, if necessary. = ? Edit y = ? Edit z = ? Edit
1 The centroid of a surface is defined by Mox ds loyds Voz ds = y=...
1 The centroid of a surface is defined by Mox ds loyds Voz ds = y= area of o area of o area of o Find the centroid of the portion of the sphere x² + y2 + z? = 4 above the plane z = 1. Enter the exact answers. - 1 2 y II 3 =
Question 9 Using Lagrange multipliers, find the point on the plane x + 3y + 72...
Question 9 Using Lagrange multipliers, find the point on the plane x + 3y + 72 = 1 that is closest to the origin. Enter the exact answers as improper fractions, if necessary. (x, y,z) = Edit ? Edit ? Edit
4. Find the surface area of part of the paraboloid z =x2 + y2 cut of...
4. Find the surface area of part of the paraboloid z =x2 + y2 cut of by the plane z = 4.
1. Find the mass and centroid of the region bounded by the = y2 with p...
1. Find the mass and centroid of the region bounded by the = y2 with p (a, y) parabolas y x2 and x 2. Set up the iterated (double) integral(s) needed to calculate the surface area of the portion of z 4 2 that is above the region {(«, у) | 2, x < y4} R 2 Perform the first integration in order to reduce the double integral into a single integral. Use a calculator to numerically evaluate the single...
Find the surface area of the part of the paraboloid z = 16 – x2 -...
Find the surface area of the part of the paraboloid z = 16 – x2 - y2 that is within the cylinder x2 + y2 = 4 and above the first quadrant. Enter your answer symbolically, as in these examples
Verify Stokes' Theorem by evaluating the line integral and the double surface integral. Assume that the...
Verify Stokes' Theorem by evaluating the line integral and the double surface integral. Assume that the surface has an upward orientation. (a) F(x, y, z)= x’i + y²j+z?k; o is the portion of the cone below the plane z=l. (b) 7 (x, y, z)=(z - y){ +(z+x) ș- (x + y)k; o is the portion of the paraboloid z=9-r? - y2 above the xy-plane. [0, 187]
find the surface area of that portion of the sphere x^2+y^2+z^2 = 25 that is below...
find the surface area of that portion of the sphere x^2+y^2+z^2
= 25 that is below the xy-plane and within the cylinder
x^2+y^2=4
5. [10 Marks] Find the surface area of that portion of the sphere x2 + y2 2-25 that is below the ry-plane and within the cylinder 2 -4
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 absolute extrema of the given function on the indicated closed and bounded set R....
Find the absolute extrema of the given function on the indicated closed and bounded set R. f (x,y) = 2x2 + 3y2 – 3x; R is the disk x² + y2 s 16. Enter the exact answers in the form of improper fractions, if necessary, Absolute maximum Edit Absolute minimum: Edit
The centroid of a surface o is defined by f= lo xd area of o y loyds area of o Do zds area of o 1 1 Find the centroid of the portion of the paraboloid z = 3(x2 + y2) below the plane z = 40. Enter the exact answers as improper fractions, if necessary. = ? Edit y = ? Edit z = ? Edit
1 The centroid of a surface is defined by Mox ds loyds Voz ds = y= area of o area of o area of o Find the centroid of the portion of the sphere x² + y2 + z? = 4 above the plane z = 1. Enter the exact answers. - 1 2 y II 3 =
Question 9 Using Lagrange multipliers, find the point on the plane x + 3y + 72 = 1 that is closest to the origin. Enter the exact answers as improper fractions, if necessary. (x, y,z) = Edit ? Edit ? Edit
4. Find the surface area of part of the paraboloid z =x2 + y2 cut of by the plane z = 4.
1. Find the mass and centroid of the region bounded by the = y2 with p (a, y) parabolas y x2 and x 2. Set up the iterated (double) integral(s) needed to calculate the surface area of the portion of z 4 2 that is above the region {(«, у) | 2, x < y4} R 2 Perform the first integration in order to reduce the double integral into a single integral. Use a calculator to numerically evaluate the single...
Find the surface area of the part of the paraboloid z = 16 – x2 - y2 that is within the cylinder x2 + y2 = 4 and above the first quadrant. Enter your answer symbolically, as in these examples
Verify Stokes' Theorem by evaluating the line integral and the double surface integral. Assume that the surface has an upward orientation. (a) F(x, y, z)= x’i + y²j+z?k; o is the portion of the cone below the plane z=l. (b) 7 (x, y, z)=(z - y){ +(z+x) ș- (x + y)k; o is the portion of the paraboloid z=9-r? - y2 above the xy-plane. [0, 187]
find the surface area of that portion of the sphere x^2+y^2+z^2
= 25 that is below the xy-plane and within the cylinder
x^2+y^2=4
5. [10 Marks] Find the surface area of that portion of the sphere x2 + y2 2-25 that is below the ry-plane and within the cylinder 2 -4
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 absolute extrema of the given function on the indicated closed and bounded set R. f (x,y) = 2x2 + 3y2 – 3x; R is the disk x² + y2 s 16. Enter the exact answers in the form of improper fractions, if necessary, Absolute maximum Edit Absolute minimum: Edit
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