find where Use the chain rule for multivariable functions to f(u, v) = u + v², u(x, y, z) = x²+y, and v(x, y, z) = 2-y %3D

Q: This is the graph of function f. 2 T -2 Y 1 2 3 4 X

A:

Q: Find My My, and (x, y) for the lamina of uniform density p bounded by the graphs of the equations. y…

A: My =ρ∫08x.x2/3dxMy=ρ288/3My=323ρIf region in the plane with constant density ρ is bounded by the…

Q: What is y(x) (i.e., y as a function of x) given that dy dx where you are given the boundary…

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Q: Q1: Find the gradient of the following function: f(x, y, z) = e* sin(y) In(z)

A: Given Function = f x,y,z = ex siny ln z

Q: prove that [L2,Lz]=0

A: L^2 is an operator that represents the square of angular momentumIt is equivalent toL^2 = L^x2 +…

Q: 1- Find the gradients of the following functions: (a) T =r ( cos0 + sin0 cosØ ). (b) F = e" sin(y)…

A: a)

Q: Infinite String: consider the initial/boundary value problem = c2 dx2 u(x, 0) = f(x), хER, t > 0, x…

A: (a) Plotting the below functions :  f(x)=1-x2x<10x>1         g(x)=0 At x=0, f(x)=1At x=±1,…

Q: Find the divergence of D for the following. 4x y2 2x -

A: Given: The vector field is given as

Q: Evaluate the surface integral /| (2xzdydz + ydzdx + z?dxdy) where S is a closed surface, given by S:…

A: Given:I = ∯S 2 xz dy dz + y x dx dz+…

Q: Graphite is lamellar crystal in which single layers of carbon atoms or graphene are distributed at…

A: Graphite is lamellar crystal in which single layer of carbon atoms. Graphene has hexagonal, 2-d…

Q: 4. Evaluate the surface integral [[ f dS where, = xz and E is the boundary of the region D in R3…

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Q: a pto -ax ikx F(k) = e*dx

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Q: Find all critical numbers by hand. f(x)=x²-23 x+5

A: Given data, Function is given as, fx=x2-23x+5.

Q: Find an equation for the plane through the points (-6, 8, –1) and (-1,3,–8) and perpendicular to the…

A: The equation of the perpendicular plane is-4x-3y+8z=0Equation of a plane is given…