dw Find ди dw, and if w = x3 + In (=) + y, x = u? –+ 5 and v = - dv v y = 3v + 5u and point (v,u)=(2,-2)

Q: The equations ry? + 6xzcos(u) + ye" = 12 and x'yz + xe" – 4u?v? = 12 are solved for u and v as…

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Q: f(x, y, z) = 4xy-8xyz + 7yz2 %3D (x, y, 2) = %3D x, y. 2) = %3D x, Y, 2) = %3D

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Q: E = {(x,y, z) E R³ |z² + y³ < z< 12 – 2x² – 2y²}. %3D

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Q: The equations xcos(u) + 6uy² +e² +2 = 0 and 2ye" + 4x²v – 3xcos(z) +1 = 0 are solved for u and v as…

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Q: dz dz Let z= f(x,y) , where x= u? + v? and y= Find and du at (u,v) = (- 40, - 4), given that :…

A: Please see the explanation below

Q: 5 Jlgu ntinuity equation satisfied by u= 3x^2-2y^2, v=-6xy IO 4xy+y?, v= 6xy+ 3y .II O U = u=x-4y,…

A: We have to solve given problem:

Q: Q3: ди ди 1. Find ди and az for u =, ifp = x+ y +z ,q = x + y +z,r = ax' əy' q-r x +y - z at the…

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Q: w csc'udu - cotu dw = 0, w(T/6) = TT CSC A. -V(3) t = w cotu B. - V(2 ) n = w cotu C. V(3) TI =w…

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Q: 8. Use change of variables to find: a) The Jacobian if x=(u+3v), y =; -(v- 2u).

A: We will use concept of change of variables.

Q: :f (x, y, 2) = x + y; E = {(x, y, z) |1 0, y > 0}

A: In this question given that a function and it is in the cartetion coordinate. We can convert in…

Q: Q 1 Find (ylz at the point (w, X,y,Z) (4,2ル-) Jy'z W = x² y? +yZ -2 tyz + 7? = 6

A: The partial derivative of the functions with multiple variables can be calculated by assuming the…

Q: X > U (M-, M+) M, Xca) 3. X(2) rimators: 2 1x

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: xyz aw aw 3) Suppose that w=e, x= 3u+v , y=3u-v , z=u'v Find du av

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Q: Find Dy, Dx and the value of x, y,z    x + y + z = 2   6x -4y+5z=31   5x +2y+2z=13

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Q: (u + v) Evaluate SS x² + y²dxdy over the square with corners (-1,0), (0,1), (1,0) and (0, -1) in two…

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Q: If u = 2x - 3y, v = -x + y. Then the Jacobian J(u,

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Q: f(x,y,z)=x+y+z and r(u,v)= (2u+ v, 3u - v, u+2v). What is the value of f(r(u,v)) r, xr, AA when u=2,…

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Q: (b) Let Y"(t) +2Y'(t) + Y(t) = 3tet, Y(0) = 4, Y'(0) = 2. Then find Y(1). %3D

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Q: y = (1,y) O A. 2uv %3D O B. a(u,v) -2uv (1,y) OC. d(u,v) O D. 0(1,y) 0(u,v) 24 E. None of the…

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Q: Evaluate I C: x-axis from (0, 0) to (0, -5) and (0, -5) to (2,-5) (2x - y) dx + (x + 5y) dy.

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Q: Evaluate 3xz dV where E = {(r, y, z) | 2 < ¤ < 4, x < y < 2x, 0 < z < x + 2y}

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Q: М %3D хеу -2, х %3D 2uv, y %3Dи - v, z %3D и + v; ƏM ƏM du' dv when u = 2, v = -2 ƏM du ƏM dv %3D II

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Q: Show mathematically that (10-6) is not independent of (10-1),(10-3), and (10-4).

A: We can write (10  -6) as:

Q: x+2 السؤال الثالث: جد ناتج التكامل (x - 4y + y* z)dydxdzباستخدام التحويل v =, u = 4y – x, W =

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Q: The equations xy² + 8xzcos(u) + ye" = 16 and x³yz+xe" – 3u?v² = 9 are solved %3D for u and v as…

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Q: b) f(x, y) = e²=²+v, u= (1,0). %3D

A: We have to find the directional derivative

Q: Q.2 Find curlF at point (1,0,0) where f(x, y, z) = xe*y + y + 2

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Q: = [x, y, v3]. Find a vz such that (a) div v > 0 everywhere, (b) div v > 0 if |2| 1

A: Given: V=[x,y,z] Formula used: div V=∇.V=∂∂xx+∂∂yy+∂∂zV3=2+∂V3∂Z

Q: Lặi T(z) = -6zª +2² – 1 and U(z) = 2 – 4z + 3 Find T(2) + U(z). %3D OA -6z + 22+-4z +2 OB -72 +2 OD.…

A: Tx=-6x4+x2-1  &amp;  Ux=2x3-4x+3

Q: 5) Find ôw/ôv if w=x² +(y/x), x u-2v+1, and y= 2u +v-2, at the point (u, v) = (0,0)

A: We have to find all partial derivatives first.

Q: dw ду Find OW at the point (w, x, y, z) = (9,3,1,1) if w = x²y² + yz - z³ and x² + y² + z² = 11. dy…

A: Given: w=x2y2+yz-z3x2+y2+z2=11 The objective is to find the partial derivative of w with respect to…

Q: u:(x, t) = и (т, Urz(T, t) u,(0, t) = uz(1, t) = 0 u(x,0) = f(x)

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Q: Find Duf at P. f(x, y, z) = 6x°y°z*; P(1, – 2, 1); u = i %3D Duf = i

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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: Саuchy Riemапn equations are и %3у апd u х у = - U y u =v and u =v х у У х .Εν and и %3Dу апd u = -…

A: The solution is given as

Q: az and ди az Given that z = exy, x = 2u + v, y = , find (using chain dv rule).

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Q: (a) F(r, y, 2) = 7+ 27 + 3K. (b) F(r, y, 2) = i + 25 + zk. (c) F(r, y, z) = xỉ+ yj+ 3K. (d) F(r, y,…

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Q: Let w = iz2-4z+3i. find (a) Δw, (b) dw, (c) Δw-dw at the point z=2i

A: Consider the provided question, (a)

Q: Q5: ди ди ди and dz p-q a. Find for u = if p = x + y + z ,and q = x + y + əx' əy q-r z, and r = x+ y…

A: Consider the given values. p=x+y+zq=x+y+zr=x+y-z And, u=p-qq-r                          (1)

Q: dz Find when u = 0, v = 1, if z= sin (xy) + x sin (y), x= 3u + 2v, and y = 2uv. ne dz ne |u = 0, v=…

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Q: The equations xy² + 6xzcos(u) + ye" = 12 and æ³yz + xe® – 7u?v² = 21 are solved for u and v as…

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Q: An unevenly heated metal plate has temperature T(x,y)T(x,y) in degrees Celsius at a point…

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Q: V(x,v,z)=5x² – 2xy+ xyz In which direction does V change most rapidly at P(5, 2, 4)?

A: to find the direction of maximum change we find divergence of the function. ∇v =…

Q: | 2.xdV where E = {(x, y, z) |0 < y < 2, 0sxs 4- y²,0<z< y}

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Q: z = x + xy, x= uv + w, y= u + veW dz az az when u = 1, v = 1, w = 0 du dv dw dz %3D du dz %3D dv dz…

A: We have given  z = x4 + x y3 , x = u v3 + w4, y = u + v ew To Find: ∂z∂u, ∂z∂v, ∂z∂w when u = 1, v…

Q: 1) 3y = 2arc tanx+c is solution D.E dx x*+1 ii) the slope of function f(x,y,z) = yx² +y²z³ +z*x$ – 1…

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Q: z = f(x, y) = r* – x²y+ 4y, r= g1(u, v) = u² + v², y = 92(u, v) = = uv.

A: Let's find.

Q: aw Find ди dw. and if w = x³ + In (-) + y, x = u? dv -+ 5 and %3D wwww y = 3v + 5u and point…

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Q: - gt V Xu u = (1,3,-3) , v = (4,0,2) e l

A: The given vectors are: u=(1, 3, -3)v=(4, 0, 2)