13. F(x, y, z) =x°zi+ xz°j + y In(x + 1) k, S is the surface of the solid bounded by the planes x + 2z = 4, y = 3, x = 0, y = 0, and z = 0 || || ZA x+ 2z = 4 y= 3 y X

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse…

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Q: 13) Consider the solid Q bounded by the surfaces S₁: z=1-y², S₂: z=x, S3: z=4-x-y, S₁: y=0, S₁: z=0…

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Q: Solve the Boundary Value Problem yet(x, t)=9yxx(x, t), 00 y(0,t)=y,(3,t)=0, t>0 yz(x,0) = 0, y(x,0)…

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Q: 5. . Find sSSzdv where D is the 2 solid bounded by xty'tz=4 and 2= 13x²+ 3y2. (" sce Cueam Come')

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Q: (b) Verify Green's theorem for |(x² – 2x y)d x+(x² y+3)d y, around the boundary e of the region y…

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Q: 1) Evaluate the line integral Fdr where F(x, y, =) = (x+3y, 2y +z, xy) and y: line segment from…

A: Here, F→(x,y,z)=x+3y,2y+z,xy and γ: line segment from (2,1,3) to (3,3,5) We need to evaluate ∫γF→dr→

Q: Volumes of solids Find the volume of the following solids.

A: The region is bounded by the curves, The region is shown in the graph given below,

Q: roblem 12. Calculate the volume under the elliptic parabolold z 4z + 8y and over the rectangle R…

A: The given region is z=4x2+8y2 and over the rectangle R=-4,4×-1,1. We have to find the volume under…

Q: could i please get help with 9a?

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Q: 14) Find the points on the surface xy- z2 = 1 that are closed to the origin. %3D

A: To find the point on the below surface that is closed to the origin. xy−z2=1

Q: 3. Find the olume of the solid generated by revolving about the line z--4 the region bounded by that…

A: Here is the solution of the given problem

Q: 5. Evaluate the line integral (r+2y) dr+x² dy where C consists of line segments from (0,0) to (2, 1)…

A: In order to solve this question by the formula of line integral .

Q: 5. If F=2xi - xj + y*k, evaluate ffLF av over the region bounded by the surfaces x = 0, y = 0, y = 6…

A: Given: F→=2xzi∧-xj∧+y2k∧region bounded by the surface x=0,y=0,y=6 and z=x2 ,z=4

Q: Show that if a two-parameter family of surfaces f(x, y, z, 1, µ) = 0 has an envelope, then the…

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Q: 2 3 3 Find the area of the surface z = = X2 + y2 3 where 0 < x 1, 0 < y < 1

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Q: 11. The solid bounded by the surfaces S : 1-1= y? S2 : y+z = 2 S3 : 1 = 0 S4 : y = 0 S5 : z = 0…

A: We will use triple integral to find volume of solid bounded

Q: 2. Find the area of the plane region bounded by y = 3x + 1, x = 1, x = 3,and the x-axis. y y = 3x +…

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Q: 43. Find f, 1dS, where s is the portion of the surface deter- mined by z = x2 – V3y that lies above…

A: Find ∫s1 dS where S is the portion of the surface determined by z=x2-3y that lies above the region…

Q: The solid bounded by the surfaces S1: −2 (z - 2) = y2 S2: x = 5 - 2z S3: x = 0 S4: y = 0 S5: z = 0…

A: Given that, A solid is bound by the surfaces, S1: -2(z-2)=y2S2: x=5-2zS3: x=0S4: y=0S5: z=0

Q: 3. The solid bounded by z = 0, z = 1 – x², z = y and 2y + z = 12.

A: Given that  Region z=0,z=1-x^2 and 2y+z=12  To form a triple integral

Q: 15.) The solid in the first octant bounded by the coordinate planes and the plane 3x + 6y + 4z = 12.…

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Q: 13) Consider the solid Q bounded by the surfaces S₁: z=1-y², S₂: z=x, S3: z=4-x-y, S₁: y=0, S₁: z=0…

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Q: 2 2 5. Find the volume of the solid bounded by the surface f (x, y) = 3x´y´ and the curves y = 2x -…

A: We will have to find the volume of the solid bounded by the surface f(x,y)=3x2y2 and the curves…

Q: 5. Given: G(x, y) = 4y¹ sin(2x³) Gyxy(x,y). What other 3rd order partials are equivalent to Gyxy(x,…

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Q: A surface x(y, z) is defined implicitly xy + yz +x'z' = 3-xZ Calculate ду

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Q: The solid bounded by y = 4, z = x², z = 2y, and z = 4.

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Q: Use the method of Separation of Variables to solve  uxx + uyy = u, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 subject to…

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Q: 11. Integrate G(x, y, z)=x√y² + 4 over the surface cut from the parabolic cylinder y² + 4z = 16 by…

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Q: ds k(4nr). dt --Select-- %3D volume dV k dt surface are ds - ). dt dV dt dV = k(4tr²). dt

A: Given evaporation rate proportional to surface area Use formula of volume and surface area to find

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

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Q: Show that 1 y - X 1. Z-y X-Z = 1. %3D alx-y) alz - x)

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Q: Sketch the solid described by the given inequalities. 0srs 8, -T/2 se S T/2, 0szs 1. 1.0 1.0 z05…

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Q: 9. The solid bounded by x = 1 – y?, z = y², x = 5, and z = 9.

A:

Q: Evaluate the surface integral. ∬Sz2dS,S∬Sz2dS,S is the part of the paraboloid x=y2+z2x=y2+z2 given…

A: Evaluate the surface integral. ∬Sz2dS,Sis the part of the paraboloid x=y2+z2 given by 0≤x≤4

Q: 2. The area bounded by y = -(x - 1)2 + 4, and the lines x =1, y = 2, and y = 4 rotated about the %3D…

A:

Q: 4. Suppose that VxF= (0,1,-1), S is the plane x + y + z = 1 in the first octant and Cis the boundary…

A: Given: ∇×F=01-1 S is the plane x+y+z=1 in the first octane  and C is the boundary of S. Now, to find…

Q: 4. Find the area enclosed by: a. y= sin(x) and y cos(x), x=0, x = and the y-axis. b. y=x and y =Vx.…

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Q: The solid bounded by the surfaces S1: 2x + 3z = 6, S2: y = 2, S3: (y − 2) 2 = 2x − 2, S4: x = 0, S5:…

A: Consider the surfaces  S1: 2x + 3z = 6, S2: y = 2S3: (y − 2)2=2x − 2, S4: x = 0S5: y = 0S6: z = 0

Q: [32] (a) Find all nontrivial product solutions u(x, y) = X(x)Y(y) #0 of Uxx + Uyy = 0 (0 < x <∞,0…

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Q: 2. Calculate the volume of the solid that is bounded by the surface x²+y²-4y%3D0, inferiorly by the…

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Q: 1. Verify Green's theorem in the plane for 6 (3x- 8y) dx + (4y – 6xy)dy, where C is the boundary of…

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Q: The minimum value of f(x,y,z) = x^2 -2y + 2z^2 on the sphere x^2 + y^2 + z^2 =1 is ....?

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Q: c, y, z) = x²zi + xz'j+ y ln(x + 1) k, s the surface of the solid bounded by the 2z = 4, y = 3, x =…

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Q: The solid bounded by the surfaces S : -2(: – 2) = y² S2 : 1 = 5– 2y S3: r=0 S4 : y = 0 Ss : z = 0…

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Q: 6. Consider the solid Q bounded by the surfaces S1 : 1 = 4 – 22 S2 : 1+y = 5 S3 : 1 = 0 S4 : y = 0…

A: Solid bounded by surfaces: Double integration can be used to find the volume of a solid limited by…

Q: Find all solutions in the form u(z, y) = X(x)Y(y) of the boundary value problem U - Uyy = 0, u(0, y)…

A: To find the solution of the given pde in the form ux,y=XxYy Differentiating u with respect to x,…

Q: 2. Find the volune og the solid gonned by revohing abaut thie lere y y=4x+1, y: -1 bounded by 4x +3,…

A: The volume for solid of revolution generated by revolving the area bounded by curves y=f(x) and…

Q: (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 - x², y = 0, and y = 4

A: Consider the given function fx,y,z=x-y.  The region E is enclosed by the surfaces…

Q: 10. The solid bounded by y = 4, y – x = 1, z = x², and z = = 4.

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Q: 2. The solid in the first octant bounded by the planes x = 0, y = 0, z = 1, z = 2 – y, and the…

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