a) Integrate g(x,y,z) = Inx²+y over the surface of the region cut from the plane 4x+3y+2z=1 by the cylinder whose walls are x+y=8 and x²-y=0.

Q: Problem 1 Describe the region of the xy-plane whose points (xo, yo) have this property: the IVP y' =…

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 3x+6y +9z 18 and the plane…

A: Now,

Q: At what points does the normal line through the point (1, 2, 1) on the ellipsoid 4x² + y²+42² = 12…

A: smaller x-value: (−15,−6,−15)larger x-value: (343​,326​,343​)Explanation:Given the equation of…

Q: Let F =   Find the outer flux of F through the surface S that is the portion of the paraboloid z =…

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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: Find the volume of the solid that lies under the plane 4x + 6y − 2z + 15 = 0 and above the rectangle…

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 9x + 18y + 27z on the elipse…

A: Using Lagrange Multipliers with Two Constraints to find the maximum and minimum values of the given…

Q: Show the triangular region bounded by the lines x = 0, y = 0 and x + y = 1 is invariant for the…

A: Given: It is given that, the triangular region is x=0, y=0 and x+y=1. To prove: We have to prove…

Q: Calculate line integral F-dr where F(x, y) = (7x + y, 5x + 2y) and C is a rectangle with vertices…

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Q: A fluid has density 600 kg/m³ and flows with velocity xi+yj + zk, where x, y, and z are measured in…

A: From the given information we get:

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: 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: Integrate f(x,y) = x² + y² over the triangular region with vertices (0,0), (17,0), and (0,17). The…

A: Given: fx,y=x2+y2. We have to integrate the given function over the triangular region with vertices:…

Q: Integrate Xy ed २ over the triangular region with vertices: (0,0), ), (0,8) (0,16)

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Q: Find all critical points of the given plane autonomous system. (Enter your answers as a comma-se x'…

A: Here is the Answer and Explanation

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 6x + 12y + 18% on the elipse…

A: subjected  to constrain

Q: The equation for a plane tangent to z = f(x, y) at a point (xo, Yo) is given by z = f(xo, Yo) +…

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Q: use the lagrange multiplier to find extreme points of f(x,y,z) = 2x+z over the intersection of…

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Q: Integrate g(x, y, z) = x + y + z over the portion of the plan 2x + 2y + z = 2 that lies in the first…

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Q: (B) Integrate paraboloid (x, y, z)=- 2x-²-2-0 by the plane x=1. over the surface cut from the end of…

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Q: Parameterize the portion of the surface f(x, y) = x² + 1 that lies inside the cylinder x² + y² = 4

A: We have to find the parameterizations of the surface

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: a) Letfx, y) = xe-y+ 5y.Find the slope of the surface z = fx, y) in the y-direction at the point (3,…

A: NOTE: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Calculate % F-dr where

A: Given,           F=xyi+2zj-xykand C is the intersection of the of the plane y=z+2 withcylinder…