F(x,y,z) = x^2z^2i + y^2z^2j + xyz k S is the part of the paraboloid z...

F(x,y,z) = x^2z^2i + y^2z^2j + xyz k S is the part of the paraboloid z = x^2+y^2that lies inside the cylinder x^2+y^2 = 16, oriented upward.

Expert Solution

milcah answered 2 years ago

The plane x + y + 2z = 12 intersects the paraboloid z = x2 +...

The plane x + y + 2z = 12 intersects the paraboloid z = x2 + y2 in an ellipse. Find the points on the ellipse that are nearest to and farthest from the origin. nearest point (x, y, z) = farthest point (x, y, z) =

Use the Divergence Theorem ∬SF⋅dS=∭D∇⋅FdV to find ∬SF⋅dS where F(x,y,z)=x^2i+y^2j+z^2k and S S is the surface...

Use the Divergence Theorem ∬SF⋅dS=∭D∇⋅FdV to find ∬SF⋅dS where F(x,y,z)=x^2i+y^2j+z^2k and S S is the surface of the solid bounded by x^2+y^2=9 , z = 0 , and z=6

Find the surface area of the part of the paraboloid x = y^2 + z^2 that...

Find the surface area of the part of the paraboloid x = y^2 + z^2 that lies inside the cylinder y^2 + z^2 = 25

1.) If A= 2i + 4j - k and B= i + 2j + 3k ,...

1.) If A= 2i + 4j - k and B= i + 2j + 3k , find the product of the two vectors. 2.) An airplane travels 209 km on a straight course at an angle of 22.5° East of North. It then changes its course by moving 100 km North before reaching its destination. Determine the resultant displacement of the airplane. 3.) Calculate the average velocity given 6.00 m and 8.00 m respectively and its time interval t= 2.00...

Consider the scalar functions f(x,y,z)g(x,y,z)=x^2+y^2+z^2, g(x,y,z)=xy+xz+yz, and=h(x,y,z)=√xyz Which of the three vector fields ∇f∇f, ∇g∇g and...

Consider the scalar functions f(x,y,z)g(x,y,z)=x^2+y^2+z^2, g(x,y,z)=xy+xz+yz, and=h(x,y,z)=√xyz Which of the three vector fields ∇f∇f, ∇g∇g and ∇h∇h are conservative?

The curried version of let f (x,y,z) = (x,(y,z)) is let f (x,(y,z)) = (x,(y,z)) Just...

The curried version of let f (x,y,z) = (x,(y,z)) is let f (x,(y,z)) = (x,(y,z)) Just f (because f is already curried) let f x y z = (x,(y,z)) let f x y z = x (y z)

Let the surface (S) be the part of the elliptic paraboloid z = x2 + 4y2lying...

Let the surface (S) be the part of the elliptic paraboloid z = x2 + 4y2lying below the plane z = 1. We define the orientation of (S) by taking the unit normal vector ⃗n pointing in the positive direction of z− axis (the inner normal vector to the surface). Further, let C denotes the curve of the intersection of the paraboloid z = x2 + 4y2 and the plane z = 1 oriented counterclockwise when viewed from positive z−...

Use the Stoke’s theorem to evaluate Z Z S (∇×F)·nˆ·dS where F(x, y, z) = (x^2...

Use the Stoke’s theorem to evaluate Z Z S (∇×F)·nˆ·dS where F(x, y, z) = (x^2 z^2,y^2 z^2, xyz) and surface S is part of the paraboloid z = x^2 + y^2 that lies inside the cylinder x^2 + y^2 = 4, oriented upwards. Sketch the surface S and label everything.

Calculate the integral of the function f (x, y, z) = xyz on the region bounded...

Calculate the integral of the function f (x, y, z) = xyz on the region bounded by the z = 3 plane from the bottom, z = x ^ 2 + y ^ 2 + 4 paraboloid from the side, x ^ 2 + y ^ 2 = 1 from the top.

Let F(x, y, z)=2xy^2 +2yz^2 +2x^2z. (a) Find the directional derivative of F at the point...

Let F(x, y, z)=2xy^2 +2yz^2 +2x^2z. (a) Find the directional derivative of F at the point (−2, 1, −1) in the direction parallel to the line x = 3 + 4t, y = 2 − t, z = 3t. Answer: 58/√26 (b) Determine symmetric equations for the normal line to the level surface F(x, y, z)= −2 at the point (−1, 2, 1). Answer: x = −1 + 4t, y = 2 − 6t, z = 1 + 10t

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