theorem find the value of f F.dr ere F(x,y) = (e* – y³)i + (cosy + x³)j and C is the nded by the rectangular region with boundary line x = | 2 and 1 -

Q: 2-) Let T be the region bounded by the coordinateaxes and the line wwm m www X+y= tin the xy-plane.…

A: Given that  x+y=π. That is the graph is y=π-x. Now the region T is bounded between this line and the…

Q: .5 f(x, y, z)dxdydz where f(x, y, 2) = x + Evaluate the triple integral 2x – y and w = 3 u = 2…

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Q: 1. Let F(x, y) = (-y,x). Let C be the boundary of the triangle with vertices (0,0), (1,0), (0,1),…

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Q: 3. Evaluate (line integral)c xz ds where C is the line segment from (0, 0, 0) to (3, 2, 6) followed…

A:

Q: (a) Find a harmonic function u(z, v) on the upper half-plane H := {(1, v) | v2 0} such that u is…

A: (a) We can write down a solution of explicitly as u(x,y)=θ3π-2θ2π+θ1π, where θi are the angles shown…

Q: Evaluate the integral 1/F. F. dr. F(x, y) = = (5x² + y) i+ (3x − cos y) j where C' is the boundary…

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Q: F= xy'i + x'yj + 9 sin(x)k; D the region bounded by the conez- and the planes z= 4, z = 6 eBook

A: Outward flux using Gauss divergence theorem

Q: 3. Find the linearization L(r, y, z) of the function f(x, y, z) = y² sin(2rz) at Po = (7,2, 4). Then…

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Q: Set-up the integral for the area A(R) of the region Rbounded by the lines y cos 2zy sin 2r and to…

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Q: (XY) Cos E lim x.y) ->(I) 1-X -Cosy lim x2 y? Cx, y)->Co.d) 2x"+y4 How Can the function = x²+…

A: We will find out the required values.

Q: 2) The region is defined by y= sin x, y = 0, x= 0, x = T. Rotate the region about the: a) x-axis b)…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

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: (sin(x-y) Ix + lyl + 이 (x, y) = (0,0) f(x,y) = } Ix+\y] Let is f continuous at the region? Why?

A: To check continuity we need to check Lim (x,y)-&gt;(x0,y0) f(x,y)=f(x0,y0)

Q: II. Find the centroid of the region bounded by the curves y = cos x, y = 0,x = 0, = x

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Q: Use Stokes's Theorem to evaluate F. dr. In this case, C is oriented counterclockwise as viewed from…

A: Using the Parametric equation of the plane.containing the triangle

Q: Find div F and curl F if F(x, y, z) = 17y®z*i – 8x'z®j – 4cy°k. %3D - div F= curl F=

A:

Q: (b) Integrate f over the given region. 1. f(r, y) = r/y over the region in the first quadrant…

A: (1) Consider the provided information, fx,y=xy And, the region is y=x, y=2x x=1 and x=2. Integrate…

Q: 11) Evaluate [[sin (y') dA , R: the region bounded by y =- Vx, y=2 & x=0

A: To find- Evaluate ∬Rsiny3 dA, R: the region bounded by y = x, y = 2 &amp; x = 0.

Q: PUse Green's Theorem to evaluate the line integral. S(x² – y²) dx + 2xy dy C C: boundary of the…

A: We have to evaluate the integral ∫Cx2-y2dx+2xydy by using Green's theorem. Where C is the boundary…

Q: g. The region bounded by: y =Vx, y32 and x=0 about y32. h. The region bounded by: y = x, y=2 and x-0…

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

Q: 29-32 Use double integration to find the area of the plane re- gion enclosed by the given curves.…

A:

Q: a) Find the maximum and minimum values of a function F(x,y,z)=8r +y +z on the surface +y'+z=18

A: Step:-1 Given that  Fx, y, z=8x +y+zx4 +y4 +z4=18 ----(1) Take gx, y, z= x4 +y4 +z4-18 Using…

Q: Using Green's theorem in the plane, evaluate (x'y dy - x²y dx), where C is the triangle with…

A: As we know that; The Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydxdy Given: I=∫Cx3y2dy-x2y3dx So,…

Q: B is counterclockwise boundary of the region that is enclosed by the x-axis, the y = x - 2, and the…

A:

Q: Find the centroid of the thin plate bounded by the graphs of the functions glx) x-1)1 and f) 1 with…

A: The given thin plate is as shown below: The region can be expressed as R=x,y:gx≤y≤fx, 0≤x≤2.

Q: a) f, if any. Let f(x, y) = 2x² + 2y² - 3xy - 2. Find the local maximum and minimum values and…

A: Given: fx,y=2x2+2y2-3xy-2 To find: Local maximum and minimum values and saddle points if it…

Q: [xcsc (y/x) - y]dx + xdy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y) = M(x,y)DX + N(x,y)dy…

A: The given differential equation is; [xcsc (y/x) - y]dx + xdy = 0

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: I need help finding the absolute maximum and minimum values of f on the set D.

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Q: 3. Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x - 2y + 3 = 0 and y…

A:

Q: Use Stokes's Theorem to evaluate F. dr. In this case, C is oriented counterclockwise as viewed from…

A: we have, Fx,y,z=2yi^+3zj^+xk^ and vertices of triangle 3,0,0,0,3,0,0,0,3 ∇×F=ijk∂∂x∂∂y∂∂z2y3zx…

Q: Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. O…

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Q: III. Let R be the region below enclosed by the curves 2 x = y + 2y, x + 5y = 0, and x = 5. Set up…

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Q: Find the generated volume f(x)=sin(x) and the lines x=0 and x=π and rotate about the x-axis V=π^2…

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Q: The integral 2n x dx (a) Identify the plane region that is revolved. O plane region bounded by x =…

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Q: Use Stokes's Theorem to evaluate F. dr. In this case, C is oriented counterclockwise as viewed from…

A: Answer is in next step. please give a like!!

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: Find div F and curl F if F(x, y, z) = x°i – 10j + yzk. div F= curl F=

A: To find the divergence and curl of the following vectorF→=x9i-10j+yzk

Q: R is the region bounded by the functions f(x) = x + 2 and the x-axis and the lines x=1 and x=4.…

A: Given: 1) The given region is bounded by y=x4+x, y=0,x=0 and x=2 about the line x=4 2) The given…

Q: Consider the function f(x) = zX - 6A Let R be the region bounded by the curves 3 y = f(x) and y = 0…

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Q: 3) A curve C is the boundary of a shaded region D which defined by y = 2x² - 4 and y = 2x in…

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Q: III. Let R be the region below enclosed by the curves 2 x = y + 2y, x + 5y = 0, and x = 5. Set up…

A: From the question, we are asked to evaluate the length of the blue curve which is x=y2+2y from y=0…

Q: oply Green's theorem to evaluate the line integral fxydx - xydy, where C is the boundary of the…

A: See the attachment

Q: The area bounded by y = 3, X = 2, y = -3 s and x = 0 is revolved about the y-axis 10. The…

A: Given: y=3, x=2, y=-3 and x=0 is revolved about the y-axis.

Q: F(x, y) = (3x2 + y i + 3xy²j C: boundary of the region lying between the graphs of y = Vx, y = 0,…

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Q: Using Green's theorem in the plane, evaluate $ (ry² dy - x²y* dx). where C is the triangle with…

A: Using Green's theorem in the plane, we have to evaluate ∮Cx3y2dy-x2y3dx, where C is the triangle…

Q: Q: Evaluate the closed line integral p y³dx – x³dy C Where C is the closed path from point A(1,0) to…

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Q: Ise Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise.…

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Q: 10 Find div F and curl F if F(x, y, z) = xz°i+ 5y"x²j+ 4z?yk. div F= curl F=

A: Solution:

Q: 13-28 Sketch the region enclosed by the given curves and area. 13. y = 12 – x², y= x² – 6 %3D 14. y…

A: To find the area bound by below curves