Find the extreme values of f on the region described by the inequality. a) f(x, y) =(x² +2y²)e*x+y s4 b) f(x.y.z)= xy+ xz, 6x +2y +z? $12

Q: A region R is bounded by the graphs of y=0.9 Vx and y=0.9x. Find the moments M, and My of R about…

A: y=0.9x and y=0.9x We have to find moments Mx and My and the center of gravity x,y

Q: Find the total area of the regions bounded by the given curve y=Vx, y=x², x=2 4/2 3 3. O 8-4/2 3 1…

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = •[ f(x) dx + [90 g(x) dx,…

A: First we identify the region by plotting (sketching) it.

Q: What is the area of the region bounded by (x – 1)² + (y – 1)² = 1? VI - (x – 1)²dæ 2 O b. None of…

A: x-12+y-12=1 The graph is,

Q: Integrate f(x, y) = x² + n xy + y² over the region: R = {(x, y): (x² + +y²)< 2}

A: First we will represent the area of the integration.

Q: 1 – x² – y? 1+x² + y² dA Where D is the region bounded by r> 0, y > 0, x² + y² < 1.

A: Dear student,  As per our company guidelines, we are supposed to solve only the first question if…

Q: (a) Consider the region bounded by the graphs of y=c(2x-4), x-1, x-3. and y 0 where c is just a…

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Q: The area of the region bounded by the curves y = sin x, y= cos x, x = 0, x = - is 2 Select one: O a.…

A: Area of region bounded by curves.

Q: (IV) The area of the region R bounded by y = x² and y = vx, le dA equals: Apxp S dxdy (b)S S xy dydx…

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = [₁ f(x) dx + ["40 + [~…

A: Here in this question, three curves are given and we need to find out the limits of integration, and…

Q: An area of a region bounded by a curve y = f(x), x axis and lines x = a and y = b for (b > a) may be…

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Q: Suppose f(x, y) = x² + y? + x?y+ 2 and D = {(x, y) : |x| < 1, |y| < 1}.

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Q: Let f(x, y) = æ² + y + xy + 4 %3| and R be the region r2 + y? <1 Find the absolute maximum value of…

A: The objective is to find the absolute maximum value of the function.

Q: 17. Region bounded by y = 2x, y = x and x = 2. Rotate about: (a) the y-axis (b) x = 2 (c) the…

A: As per company guidelines we are allowed to solve maximum three sub parts so i am solving first…

Q: Let f(x, y) = ay + 1. Find the absolute maximum value and the absolute minimum value of f(r, y) on…

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Q: 3- calculate SSm xe' dxdy -if the bounded set M is given by inequalities y <2 - x, y 2 x². -Draw the…

A: The region y≤2-x isThe region y≥x2  is The region M is,

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

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Q: Consider the region on the 1st quadrant bounded by y = √4x²,x and y- axes. If the region is revolved…

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Q: Consider the region on the 1st quadrant bounded by y = √4x²,x and y- axes. If the region is revolved…

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Q: The aren of the region bounded by y = v9 -x, the x-axis and the line y-x in the first quadrant is: O…

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Q: Given: region R below bounded by the graphs of y = = Vx – 1, y = 3 –- x, and = 0 (2, 1) R (1, 0) (3,…

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Q: Using horizontal strips, which of the following gives the area of the region R bounded by y=2+x-x²,…

A: Explanation of the answer is as follows

Q: Consider the region bounded above by the function z = 1/(x+3)2(y+7)2 and below by the xy plane for x…

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Q: The region R is bounded by the x-axis, yaxis, and the line in che graph. Then f(z, v)đydz+ f(z,…

A: We will find out the required values.

Q: The extreme values of Ax, y) = 4x + 2y? on the region x +y <4 are %3D O A. Maximum = 24, Minimum = 0…

A: Consider the given function whose extreme values is to calculate.

Q: graph of the region of integration. • 3x/4 : | f(r,0) r dr do ? v 1. A в 7/4 2x ? v 2. 2 3x/4 ? v 3.…

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Q: 17. Region bounded by y = 2x, y = x and x = 2. Rotate about: (a) the y-axis (c) the x-axis (b) x = 2…

A: Since you have posted multiple questions i can do first three subparts as per our company guidelines…

Q: integrate ƒ over the given region. ƒ(x, y) = x/y over the region in the first quadrant bounded by…

A: Given

Q: The region is bounded by y = x³, y = 2x + 4 and y = −1. Then Area region = [ f(x) dx + √ f(x) dx +…

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Q: e a region bounded by the four planes x = 0, y = 0, z= 0 and x + y + z = 11. Evaluate SSS 24x dV ov

A: See the details solution in below

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

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Q: = 0, y = x, and x = 5. n, the region D expressed as type I is: = {(x, y)|0 ≤ y ≤ x,0 ≤ x ≤ 5} ect…

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Q: Example 16. Find the volume of the region D enclosed by the surfaces z = x² + 3y² and z = 8 – x2 -…

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Q: 13. Region bounded by: y = 4 – x and y = 0. Rotate about: (a) the x-axis (c) y = -1 (b) y = 4 (d) x…

A: The solution are next step

Q: Evaluate ff, f(r, y) dr dy, where R is the region given by 0 <r< 4:0<y53 and f(z, y) 1- - }y Give…

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

A: The region is bounded by y=x3, y=2x+4 and y=-1. Then Arearegion=∫abfx dx+∫bcgx, where a&lt;b&lt;c.To…

Q: 66. The region D bounded by x= y2 - 1 and x = V1 – y? as given in the following figure. YA 1.5 x -…

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Q: Suppose the region R is bounded by y = 0, y = x, and x = 1. Evaluate: 4.x2 dA =??? 1+x4 R 2.0 1.5 dy…

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Q: While evaluating the area of the region bounded by two curves Vỹ = x and y - 11z + 24 = 0, the…

A: Given: Two curves y=x and y-11x+24=0 are intersecting each other. The objective is to find the…

Q: The value of the double integral // (2x²y + 9y') d A, D where D is the region bounded by x and y = 2…

A: Given problem:-

Q: Integrate f(x, y) = x over the region bounded by y = x 2 and y = X + 2.

A: This is the region. x2 = x + 2   x2 - x-2 = 0 x = 2 or x = -1 so , to integrating in the region.…

Q: | 5z2 dV , where E is Evaluate E the region bounded below by the cone z = Vx2 + y² and above by the…

A: Given: ∫∫∫E5z2dvz=x2+y2x2+y2+z2=1

Q: 13. Region bounded by: y = 4 – x and y = 0. - Rotate about: (а) the x-axis (c) y = -1 (b) у — 4 (d)…

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Q: To determine the area of the region bounded by y=x2 + 1 bounded by x=2, x= 1, y = 0, use a…

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Q: 55. The region bounded by y = Vx, y = 2x – 15, and y = 0 %3D

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Q: (b) Use Green's Theorem to evaluate ſ. 3ysin(x)dx + 5xdy where C is the boundary of the region…

A: Solution:Given∫c3y sinx dx+5xdyFormula:∫cPdx+Qdy=∬ ∂Q∂x-∂P∂y dA

Q: 10. The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = [*f(x) dx + [° g(x)…

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Q: Find the absolute maximum and minimum values of f(x, y) = 4 + 2x2+y2on the region R={(x,…

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

A: