Cvaluate AP G is a solid in the first octant bounded by the plane y+ z = 2 and the urface y = 1 - x².

Q: Assume S is the surface x1000 + y8000 + z1000 = 1,000,000 and F = [9 + ee^(xyz), x8yz, 3x - 5y -…

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Q: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

A: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

Q: For a given surface z-x^2-y^2=10 Find the parametric representation of the straight line which…

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Q: Calculate :/ F. ds, where F (x, y, z) = (-6x³ + 2yz)i + (-6y³ + sin¯¹ (3xz)) j+ (2z+cos (3x²y²)) k…

A: Given F(x,y,z)=-6x3+2yzi^+-6y3+sin-13xzj^+2z+cos3x2y2k^ and S is the outward-oriented surface of the…

Q: Determine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant.

A: Given surface is 9x2+4y2=30 and plane is  9x+4y-6z=0 Bounded region in first octane ⇒x≥0, y≥0, z≥0…

Q: Let T be a triangle with the vertices (0,0), (1,0) and (1,2). Also, let V be the volume of the solid…

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Q: C:1-1,4), (1,2) (-レ-1),(ル-) the boundary of the rectonale that accepts points as a corner…

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Q: Find the area of the vertical wall whose base is the semicircle {(x, y) | x² + y² = 1 and y>0} and…

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Q: Evaluate exp{}dA where R is the region in the ry-plane bounded by the trapezoid with vertices (0,…

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Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

Q: Suppose f(x, y) satisfies the basic existence and uniqueness theorem in some rectangular region Rof…

A: Consider the given: Let the function f(x,y) satisfies the basic existence and uniqueness theorem in…

Q: F(1, y.:)= (x², 2x²y*, 5yz*) Given: Find (a) div F (b) curl F

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Q: you know that a sphere has the equation of  x^2 + y^2 +z^2 -6x +4z =3 are the following points…

A: The equation of sphere is:-Now add 9 and 4 both side:-

Q: Graph the solid that lies between the surface z= 2xy/( x2 + 1) and the plane z =x + 2y and is…

A: Given surfaces are z=2xyx2+1, z=x+2y  and are bounded by planes x=0 , x=2 , x=-1 , y=0 , y=4. To…

Q: Find the points on the ellipsoid x² + y²/4 + 2²/9 = 1 that is closest to (1, 2, 3).

A: Let (x, y, z) be the points in the ellipsoid closest to (1,2,3) then using the distance formula…

Q: termine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octan

A: The given solid is bounded by the surface 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant.

Q: Determine a region of the xy-plane for which the given differentail equation would have a unique…

A: Given differential equation (y-x) y'=y+x   or    (x+y)dx+(x-y)dy=0 Note that differential equation…

Q: Let F = –9zi+ (xe"² – 2xe³) }+ 12 . Find ſg F ·dÃ, and let S be the portion of the plane 2x + 3z = 6…

A: The vector field is F→=-9zi→+xexz-2xex2j→+12k→ The equation of the plane is 2x+3z=6⇒ gx, y=6-2x3.…

Q: Evaluate the solid bounded by 2x+z=2 and (x-1)2+y2=z.

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Q: (b) Integrate (x, y,z)=(y+z)+1 the paraboloid 4x - y-z -0 by the plane x 1. over the surface cut…

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