Let f(x,y,z) = zIn(x³ycos(z)), find Z 3x² O In(x3ycos(z)) - ztan(z) 0 2 Y о 3z X af ila

Q: Let w = xydx + 2xdy - ydz E 2'(R) and let a: R a(u, v) = (uv, u², 3u + v). Compute do, a*o, d(a*o),…

A: Given ω=xy dx+ 2x dy - y dz in Ω1ℝ3x,y,z And let α:ℝu,v2→ℝx,y,z3 be given by  αu,v=uv, u2, 3u+v. To…

Q: f(x, y, z) = xy°z +x*yz² – sin xy + cos yz Which of the following is the 1st order derivative of the…

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Q: Let f(x, y, z) = ln () Vxy – sin (cos (zy)) , evaluate ху %3D дх ду

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Q: f z-3x2- 4хy3 +6х,find. дудх

A: Given z=3x2-4xy3+6x we have to find ∂2z∂y∂x

Q: e /// 2 Evaluate 2xz dV where E {(x, y, z) |1 ≤ x ≤ 4, r ≤ y ≤ 2r, 0 <z<x+3y}

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Q: The joint pdf of X and Y is given by fx,y(x,y) = {4x2   0<y<x<1}…

A: Sol:- To find the support of U, we first need to find the range of values that U can take

Q: Let f(x,y) = and let g(x, y) 4xy¹ 4x4 + 4y4 0 if(x, y) = (0,0) 0 if (x, y) = (0,0) 5xy 10 5x² + 5y20…

A: f(x,y)=4xy44x4+4y4if (x,y)≠(0,0)0if (x,y)=(0,0)g(x,y)=5xy105x2+5y20if (x,y)≠(0,0)0if (x,y)=(0,0)

Q: اجب عن السؤال - ODE dy _ (x² + y²) dx x2 Y + x²y = c x² + y²x = c 3 x2 +y?x = c 3.

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Q: Q2. If f(x, y) = xy² + y²cosy + xsiny then a) y² - siny c) 2y + cosy a²f is дудх b) y² + cosy d) 2y…

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Q: Let f(x, y) = and let g(x, y) O O rºy6 26+y6 O 0 0 6x³y³ 6x6 + 6y6 Which of the above functions are…

A: fx,y=x6y6x6+y6if x,y≠0,00if x,y=0,0 gx,y=6x3y36x6+6y6if x,y≠0,00if x,y=0,0

Q: z = f(a + y, 2ry) f we take u = x' + y' and w = 2xy we obtain z, = 2xf, + 2yf, and z, = 2yf, + 2xf.,…

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Q: *f(x,y) = xy + aS lšl fry.fyx gl y²+1

A: Given fx,y=xy+eyy2+1

Q: Prove that if Y:nz+P(x- mz) So thdz

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Q: If U(x, y) = -e-Y sin x andf(z) = U(x, y) + iV(x, y) is analytic, then f(z) = %3D O None of them…

A: Solution

Q: Let g(x, y) = x4 + y² – 4x³ + 5x – 6y+3. Show that g(x,y) continuous (actually at least aC')…

A: Recall [ Implicit Function Theorem ]

Q: Show in each case that f is differentiable at each a = (a,b) E R²: (a) f : R² → R with f(x, y) = x +…

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Q: B. Let z- ( x-y)exy Show: Zxx + zyy + e x9 Cy 3- x³)- -z (xy+ 2)

A: Given that                       z=(x-y)exy

Q: Let r = x² + y – z and z³ – xy + yz + y³ = 1. Assume that x and y are independent ar is variables.…

A: Introduction :

Q: 1. Let f(x, y) = x cos (x²y). find: af a) ƏH b) of evaluated at (s) our (show you work)

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Q: Show that (6.g) = (0,0) is unijomy continuous or not.

A: Uniform continuity

Q: 1) 10 E' F' E D' D -10 10 C -10 Which rule yields the dilation of the figure CDEF centered at the…

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Q: Let F(x , y , z) = g(y) + h(z) + 5 In(x - 2) , where g(y) and h(z) are differentiable functions of…

A: If a function is a function of more than one independent variable then the derivative of this…

Q: Please take turns to work on the following questions: 1. Let f(x, y) = x² + 3xy + y² Compute (a) af…

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Q: =grating

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Q: f (x, y) = 6xy² for 0 <x<1 and 0<y<1 and f (x, y) = 0 Calculate fx (x) and fr(y) Ny looking at the…

A: If x and y are two continuous variables then f(x,y) is called joint probability density function.…

Q: Let f(x, y) = 6e sin(7y) af af dy

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Q: z = (x + 4y) e²+y, x = In(u), y = v, find dz/du and ðz/dv. The variables are restricted to domains…

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Q: If f(x, y) = (8x2 + 8y³)³, then f_(0,0) %3D %3D A) 0 B) 2 C) 8 D) 1 E) Does not exist

A: Let us consider the two variable function f(x,y) Partial derivative of the function with respect to…

Q: if f(x, y, z) = ze +ln(y) + y²x df² dz² at point find fzz (0, 1, 1) A)10 B)2 C) - 2 D) 1

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Q: f(2) = u(x, y) + jv(x, y) v(x, y) = sin x cosh y f (0) = 0.

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Q: 5. Verify Gauss's theorem for D = {(x, y, z): 0 ≤ z ≤ 9-2²-y²} and F ri+yj + zk.

A: The given problem is to verify the gauss theorem for the given surface 0&lt;z&lt;9-x2-y2 for the…

Q: 2: find fr, fy, and fz.

A: Given fx,y,z=e-xyz to find fx differentiate with respect to x fx=e-xyzyz