Evaluate O ry*dx + a dy, where C is the rectangle with vertices (0,0), (4,0), (4,5), and (0,5) -4020

Q: Evaluate O xy?dx + a°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3)

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Q: Calculate F . dr, where C is the square of (1,1, 1), (–1,1, 1), (-1,–1,1) and (1,–1,1), with…

A: Let F→x,y,z=zex-yezi→+2cosy-xezj→+ex-xyezk→ and C is the square with vertices…

Q: Convert the integral  0∫2 0∫2z y∫2y dxdydz in the order a) dzdxdy b) dxdzdy

A: Given: ∫02∫02z∫y2ydxdydz

Q: Iculate O F- dĩ, where C is the square of (1,1, 1), (–1, 1, 1), (–1, –1,1) and (1, –1,1), with…

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Q: Describe how to find the Jacobian of x and y with respect to u and v for x = g(u, v) and y = h(u,…

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Q: Let fxy (x, y) = 6 (x – y) , 0 < y < x < 1. If E (X) = , E (Y) = Cov (X, Y) = then %3D

A: Given,fXY(x,y)=6(x-y) ; 0&lt;y&lt;x&lt;1E(X)=34E(Y)=14

Q: 1. Find a non zero unit vecor ôî that is orthogonal to u= (1,2,1) and Uz= (2,5,4) in R³.

A: Let's find non zero unit vector.

Q: Find div F and curl F if F(x,y, z) = xzºi+ 5y°x²j+ 5z?yk.

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Q: Evaluate | (transparent gamma symbol) ∫(x2 + y2) dz | where z = x + iy with (transparent gamma…

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Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (5,0,0), (0,2,0), and (0,0,4)

A: # Given integral is      ∫∫E∫ zdv

Q: Q4) Using Green's theorem to evaluate: (12 marks) Sc [ (x3 – xy³)dx + (y³ – 2xy) dy] Where C is the…

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Q: Find div F and curl F if F(x, y, z) = 10y³zºi – 8x³z¹ºj – 5xy³k. div F= curl F=

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Q: Find div F and curl F if F(x, y, z) = 9y¹zºi – 14x³z7j — 5xy³k. div F= curl F=

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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: - 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: (c) Use Green's Theorem to evaluate 3xy dx + 2xy dy, where C is a counterclockwise oriented…

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Q: du If u = x²y + y²z + z?x then at (1,1,0) is ax %3D -

A: Given that u=x2y+y2z+z2xTo find :∂u∂x  at 1,1,0Solution :u=x2y+y2z+z2x∂u∂x=2xy+0+z2∂u∂x=2xy+z2

Q: Find the Jacobian w/ respect to UVW X=U(3-v), Y= uv(3-w), Z=Uw

A: Our aim is to find the jacobian of x=u(3-v), y=uv(3-w) and z=uvw⇒x=3u-uv ,   y=3uv-uvw and…

Q: 5. Evaluate f (x²zdx – yx²dy + 3dz) where C is the boundary of the triangle with vertices (0,0, 0),…

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Q: Find the linearization L(z, y, z) of the f(x, y, z) = 2,/z° + y° + z° at the point (1, 2, 3). %3D…

A: Consider the provided function, fx,y,z=2x3+y3+z3 At the point 1,2,3 find the linearization. The…

Q: Use Green Theorem to evaluate P xydx+edy where Cis C the path from (0,0) to (1,1) along the graph of…

A: The correct option is (d). Partially differentiate M and N w.r.t y and x respectively.

Q: а. Иух — их + uy — и — 0 Uyx Их + иу — и — 0 и 3D

A: Solution a: Given partial differential equation is uyx-ux+uy-u=0 Let ux=D, uy=D'…

Q: let z- 57 dy .. dy By chain Ruie

A: The objective is to find the second derivative using chain rule.

Q: Use Green Theorem to evaluate $ xydx+e'dy where C is the path from (0,0) to (1,1) along the graph of…

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Q: + (xytl) Determine the Linearity of this DE. * ya dy y dy O Linear O Non-Linear

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Q: calculate div(F) and curl(F). F = (xy, yz, y² – x³)

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Q: Let C be the positively oriented square with vertices (0, 0), (3, 0), (3, 3), (0, 3). Use Green's…

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Q: Use Greens Theorem to evaluate: §. (2x + ev´)dy - (4y2 + e*")dx where C is the boundary of the…

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Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,3,0), and (0,0,5)

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Q: Consider, 21u = 2x – 3y and 21v = -–x+y Find the value of the Jacobian a (x, y) a (u, v)

A: 21 u = 2x - 3y, 21 v = -x + y

Q: Let C1 be the line segment from (1,0,1) to (0,3,6). Evaluate dx + dy + dz.

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Q: Draw the region = {(r, y) : 0< rs1:1-rSy<2 - (r- 1)2} U {(z, y) : 1<1<2:1-1syS2-(r-1)2} %3D No…

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Q: z dV, where E is the solid tetrahedron with vertices (0,0,0), (2,0,0), E Find (0,6,0), and (0,0,3)

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Q: 4. Let f(x, y, z) = e² + zy² and let C be a straight line segment connecting the points (4,2,1) and…

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Q: can u help me with pullbacks and integration plz

A: Given that the integral,

Q: If w = f(u, v), u = x + y, and v = x - y, show that w,wy = w - w?. %3D %3D

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Q: Find ∂U/∂T and ∂T/∂U when ((TU −V )^2)ln(W−UV) = ln(2) at the point (T,U,V,W) = (1,1,2,4).

A: Given that: TU-V2 ln W-UV=ln 2  We have to find ∂U∂T and ∂T∂U at the point T, U, V, W=1, 1, 2, 4

Q: Let C: |z-i=3 and I = §. dz 2z dz. Then %3D

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Q: 1+iz if w= Find the image |z|<1 1-iz

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Q: 2. If o = x²yz³ and F(x,y,z) = 3yzi + x²j + (x cos y)k, find: a) grad o %3| b) div F c) curl F

A: Given:  φ=x2yz3F→x, y, z=3yzi→+x2j→+x cos yk→ To Find:  a grad φb div F→c curl F→

Q: az Use the Chain Rule to find at for z = In(x? + y), x = st, y = t/s.

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Use Green's Theorem to evaluate x' dx + xy dy where C is the triangle with vertices (0,0), (1,4),…

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Q: 1. Use a change of variables to evaluate [[ y- dA where R is the trapezoid with vertices (1,0,…

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Q: 3.use Greens theorem s (1+x5 dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0),(1,3)…

A: Apply greens theorem

Q: Evaluate JI (x* +y)dxcdy on B region using the transformation 1= xy and v= x²- y xy= 2 = شر هړ. B و…

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Q: Find ff -6xydA over the D triangular region D with vertices (0,0) (2, 0), (0, 4)

A: problem is related to double integration

Q: Use Gramer's Rule to Find K,y and Z -y-22 = -8 %3D + 32 = 2 %3D 7X +y+Z = 0

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (5,0,0), (0,6,0), and (0,0,3)

A: This question is related to triple integral, We will solve it using given information.

Q: If Ø : R3 → R3 be defined as Ø (x,y,z) = (2x, 4x –y,2x+ 3yz) then show that Ø is invertible. %3D

A: Given that ϕ:R3→R3 is defined as ϕx,y,z=2x,4x-y,2x+3yz. Now, ϕ is invertible if ϕ is one-one and…