Let I = , zdV ,where D is bounded by the planes x = 0, %3D 6. z 0, x+y = 2 and the cylinder x2 + z2 = 1 in the first octant , then I = %D 6. -2-x (A) S*z(V1- x?)dzdx 1-x2 (B) z(2 - x)dydx V1-x² (C) SM-* z(2 – x)dzdx (D) S*** z(2 – x)dxdz (E) S z(x² + z?)dxdz

Q: 1) Find the volume of the prism whose base is the triangle in the xy-plane bounded by the x-axis and…

A: To find the volume of the prism described we just need to evaluate the given double integral…

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A: Given: y=2x+6 y=2x+1 y=-3x+6 y=-3x+1

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Q: A region R is bounded by the graphs of  y=0.8 (x)^1/2 and y=0.8x.  Find the moments Mx and My of R…

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Q: D Evaluate xy dady where D is Hie region bounded x=0, y=0, and x+y= ! by

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

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Q: Evaluate (2r+y) dV _ where V is closed region bounded by the z= 4>x and the planes x = 0, y = 0 and…

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Q: Suppose that f (x, y) satisfies f(-x,y) = –f(x, y). Give an /| s(x, y) dA = 0. example of a region D…

A: As per our guidelines we are supposed to answer only One question if there are multiple questions…

Q: Let S be the portion of the cylinder z = 1 − x2, in the first octant and between the planes y = 0…

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Q: 2) Use a change of variables to evaluate ff, zdV; where D is bounded by the paraboloid z = 16 – x² –…

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Q: [a, b] × [c, d] × [e, f], show that " S" S. f(x, y, z)dzdxdy = [" S"S, f(x, y, z)dzdydx by…

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Q: A clamped cubic spline S for a finction fis defined by a(x - 3) + (x-3)²+b(x – 3)³ - 2(x-4)-5(x -…

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Q: Let A = { (x,y)e RXR; 0<max{}x-31. ly-21)<1}, then: %3D None of the choices OA is not compact…

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Q: find thearea of the. region.. R bounded. b. the. graphns. Of. the gienequations. y x-1j y=0, X= 2…

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Q: 3)Evaluate /y² + 1dA , Ris bounded by x = 4 - y² ,x = 0 R

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Q: 1) Evaluate the integral SRW (x,y,z)dV with W= e*-y-z where R is a rectangular box with corners at…

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Q: (c) By using the Green's theorem, evaluate $(2xy) dx + (4x²y*) dy if C is the boundary of a region…

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Q: 4. If R is the total resistance of three resistors, connected in parallel, with resistances R, R,,…

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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…

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Q: Use Green's Theorem to evaluate: • dr C where F = (Vx + 3y, 2x + 3y) and C is the boundary of the…

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Q: Let I = [[, ydV ,where D is bounded by the planes y = 0, z = 0 , x+ y = 5 and the cylinder y2 + z2 =…

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Q: 1. Solid S is bounded by the ff. surfaces. Sketch S and label its boundaries. 2y+z+x= 4, 2y+z+x=6,…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Fimd the Valume of the Solied oblaimed by nelating the where Ris bounded by y= x* -2,X=2,X=4 and y=0…

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Q: with vertices (0, 0), (5, 0), (5, 5). 4. f(x, y) = 4xy – 8x – 4y + 5 on the triangular In Exercise.…

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Q: 1) Find the centroid of the region that is bounded by the line Y = 3X, the line X = 2 and the X…

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Q: 3. Suppose that f and g are integrable and that f(x) dx = -1; , f(x) dx = 5; and f, h(x) dx ='4,…

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Q: 1. Solid S is bounded by the ff. surfaces. Sketch S and label its boundaries. x = y² + ²-4,…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Use Green's Theorem to evaluate nds, where F = (Va+ 3y, 2a + 3y) C is the boundary of the region…

A: Given Vector field is  F=x+3y, 2x+3y Comparing with F=P,Q, we get  P = x+3y            and…

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A: Given: The function, f:ℝ3→ℝ defined by fx,y,z=x2+y2+z2 and the region R:=x,y,z:x≥0 and x2+2y2+3z2≤3.…

Q: If F =(2 - 3:) i - 2xy j – 4xk, then evaluate [, Vx F dV, where V is the closed region bounded 3. by…

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Q: Let F(r, y, z) = r²i+ y²j+ z²k and S the surface of the region bounded by 5. the cylinder 1? + y² =…

A: Divergence theorem

Q: 3. Let g(x,y) = Vy+1 In(x + y ) . 5 (a) Find the region D in R which is the domain of g. (b) Make a…

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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: The centroid of the region bounded by sin x < y< cosx, and 0<x<7/4 is, TV2-4 b) 1 1 a) 4(42 +1) 4(v2…

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

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Q: b) A solid G is bounded by the planes y + z = 4, z = 0, y = 0 and y = 4 – x2. Evaluate dV 4 – Y G

A: Given that  A solid bounded by the planes of y+z=4,z=0,y=0 and y=4-x^2  To evaluate the integral

Q: 1. Solid S is bounded by the ff. surfaces. Sketch S and label its boundaries. z = x² + y² − 4, z = 8…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 5. Evaluate z dV, where E is bounded by the cylinder y? + z2 = 9 and the planes x = 0, y = 3x, and z…

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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: 1. Solid S is bounded by the ff. surfaces. Sketch S and label its boundaries. x = y + z −4, x=8-5ỷ…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Verify Green’s Theorem for F⃗ = , where C is the boundary of the region bounded by x = 0 , y = 0 ,…

A: Given that F=3x2-8y2,4y-6xy bounded by x=0,y=0,x+y=1Verify green's theoremGreens theorem is∫C…

Q: 10.Calculate the double integral ffRXsinydydx, where R is bounded by y=0, y=x2, x=1.

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Q: Let ECR³ be the region in the first octant bounded by z = 1 - y² and 2 = 1 x². Determine SSS 2x dV.

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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: Evaluate // (1+x² + y2) dV, where E is the region bounded E by the surfaces z = 6y2 - 9x², and z = 6…

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Q: Evaluate the triple integral [[Scosys3 12xy²z³ dV_over the rectangular box G define by the in…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.