Q2: f(x. y)- x/y over the region in the first quad- rant bounded by the lines y x,y 2x,x 1,x-2

Q: S.(2x° +5y )dx+(2x-4y') dy C:boundary of the region lying between the graphs of x² +y² = 16 and x +y…

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Q: 3. Determine the absolute maximum and minimum values of f(x,y) = 2+4x-2x²+4y-y² %3D on the region R…

A: We have to solve given problems:

Q: Rotate the region bounded by x = y² – 6y + 10 and x = 5 about the y-axis

A: Solution :-

Q: 2. Evaluate f (3x + 4y2) dA, where R is the region in the upper half-plane 15 bounded by the circles…

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Q: ex: Evaluate SS (&++y²)dV over the first octont region boundeol by the cylinders x*ty=/ and xay=4…

A: Convert coordinate system into cylinder coordinate system. Sketch region D and find range of…

Q: The area bounded by the curve z 4y+7, the y-ax y =0 and y 2 is dy3D O 18 22 11 O 15

A: Area bounded by the curve can be calculated as

Q: 1. Under the paraboloid = 3z2 + y? and above the region bounded by y = x and r= y² – y

A: Find point of intersection of:  y=xx=y2-y y=y2-yy2-2y=0y=0,2

Q: Evaluate E=∭D(x2+y2+z2)−3/2dV where D is the region bounded by the surfaces x2+y2+z2=9 and…

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Q: d. .2 The solid bounded by the cylinder x+y = 9 and the planes z = 0 and z = 3- x. %3D

A: The solution of the problem is given in the next steps.

Q: Rotate the region bounded by y = 6e 2" and y = 6+ 4x - 2x between a = 0 and a = 1 about the line y =…

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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: (b) y T= x (p) 3. Region bounded by: y = 4 – x² and y = 0. Rotate about: (a) the x-axis (с) у — —1

A: I have solved the first part for next parts repost the question

Q: Hw.3 3 Find the areas for the following Vegions: Region boundded by y=x y , and Region bounded by…

A: To find the area of the following region :-

Q: The area bounded by the curve y3a and the lines z 4 and a-9 above the z-azis is aquare units O 27v0…

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Q: Q3)Verify the Greens theorem to the integral f(2x*y-x)dy +(2yx- y)dx where C is atriangle its…

A: Green's theorem

Q: - The region bounded by y = 2 -x, y = 0, x = 1, x = 2 is rotated about the x axis. 197/12

A: volume generated by revolution of the solid is 19π12 detailed solution with explanation is given…

Q: 9. Evaluate 18x dV where E' is the region behind the surface y = 4 - 2² that is in front of the…

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Q: 9. Use Green's Theorem to evaluate (e* +y²) dx +(e" +x²) dy where C is the boundary of the region…

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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: Evaluate: ∬ 〖4X d A〗 over the region R bounded by the parabola Y = X ^ 2 and the line X = Y-2.

A: Plotting the Curves on X and Y-axis : y = x2 ...............(1)y = x + 2 ..............(2)After…

Q: 3. Determine the absolute maximum and minimum values of f(x, y) = 2+4x-2.x²+4y-y² on the region R…

A: The given function is f(x, y)=2+4x-2x2+4y-y2 The function is on the region bounded by the x-axis,…

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = S [² f(x) dx + √° 9( g(x)…

A: Given the region is bounded by y = x3 , y = 2x+4 and y = -1. Intersection of y = x3 and y = 2x+4 is…

Q: 2. A cafe estimates a monthly profit (in thousand pesos) of P(x, y) = 27 – x? – y² + 6y if they open…

A: Given: A cafe estimates a monthly profit, P(x, y)=27-x2-y2+6y and the region D=x, y∈ℝ2 : x2≤y≤4. To…

Q: The numerical value of f3dA 3dA (where D is the region bounded by lines y=0 and x= 1 and the…

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Q: Find the bounded solution of âyở y x> 0, t>0 where y (0, t) = 1, y (x, 0) = 0.

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Q: (iii) Sf xy²e*dA, Dis bounded by y = x,y = 2,x = 0.

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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: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion= = ["5(x) f(x) dx + dx +…

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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: Consider the region bounded by the Xxy curves J 3-2x, and y=3, %3D

A: Calculating the area of the region bounded by the curves

Q: Lây ởy - Find the bounded solution of- ,x>0, t> 0 where y (0, t) = 1, y (x, 0) = 0.

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Q: Compute 6xy da dy, where D is bounded by the curves y = 4 – x2 and y = 2x + 4.

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Q: 4. Find the absolute maximum and minimum of the function on the given closed bounded region. y…

A: Given function is fx,y=ex2-4x-2y+y2 Closed region is x=0,y=0 and x+y=3 The objective is to find the…

Q: 2. Evaluate [(3yz)dV where B is the region in the first octant lying below the plane x + 2y +2: = 4.

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Q: 4. Evaluate ||| x y dV , where E is bounded by the parabolic cylinders y = x², y' = x and the planes…

A: The region E is bounded by the parabolic cylinders y = x2, x = y2 and the planes z = 0 and z = x +…

Q: Evaluate fff 12y - 8x dV wherein the limits of integration are the region behind y = 10-2z and in…

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Q: f(x, y) - x/y over the region in the first quad- rant bounded by the lines y = x, y = 2x, x = 1, x =…

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Q: 5) Find the region in the xy-plane for which (sin x – y)y' = vx- y satisfies the nonlinear existence…

A: A differential equation  y' =f(x,y) will have at least one solution in the region where f(x,y) is…

Q: Let f (x, y) = y³ + x² – 3y (a) Determine all the critical points of f. (b) Determine the absolute…

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Q: The numerical value of л за 3dA (where D is the region bounded by lines y=0 and x = 1, D and the…

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Q: R Be denned by J (, 9, · Explain why we can always find the maximum and minimum of f(x, y, z) in the…

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Q: If f(x, y) is continuous, then it must have an absolute maximum in the region x? + y² < 1. True…

A: Given: f(x,y) is continuous Region R is an open circle centre at origin and radius 1 ie x2+y2 &lt; 1…

Q: 2. Evaluate , dV, where o= 45 x²y and V is the closed region bounded by the planes 4x + 2y +:=8, x=…

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Q: Q4 If F=2zi - xj +yk, Evaluate ff, F dv. where v is the region bounded by the surfaces: x-0, y-0,…

A: The detailed solution of the problem is given in the next step.

Q: 1 Integrate the function f (x, y) = over the region bounded by r-axis, line æ = 7, and the curve y =…

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Q: O R is the region bounded by y = 2 – x² and y = x² – 6. - %3D

A: 5.)  y=2-x2  and  y=x2-6 red line y=2-x2 blue line y=x2-6

Q: 4x Estimate the error in the quadratic approximation of f(x,y) = e sin y at the origin over the…

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Q: O R is the region bounded by x² + y – 4 = 0 and x – y +2 = 0 an is revolved about y = 0.

A: We use washers method to find the integral of that evaluate the volume of the solid of revolution.

Q: Let f (x, y) = y³ + x² – 3y (a) Determine all the critical points of f. (b) Determine the absolute…

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Q: b) Evaluate [[ (3-4x)dV where E is the region below :=4-xy and above the region in the xy -plane…

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