Let Y have the density f(y) T(a+B) ya-1 T(a)r(8) (1+y)ª+ß" y > 0, determine E(Y) and E(Y²).

Q: Let z = f (x, y) where a = g(t) and y = h(t). Find , when t = 1 given that dt g(1) = 3, h(1) = 2, g'…

A: Take the derivative and Substitute the given values than simplify.

Q: x tan(yz) ey – 4x3z2 3: Find the total derivative of f(x, y, z) =

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Q: Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

A: Given: f (x, y) = xy2 + 5.

Q: 1. Given function f(x,y) = xy ln(x + y). Find (a) fr(x,y) = (b) f,(x, y) : (c) fææ(x, Y) = (d)…

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Q: Consider the IVP: 1 y"(t) + 2y'(t) + 2y(t) = 1², y(0) = y(0) = 0 (a) The complementary function yo…

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Q: Given the continuous function: (a) f(x, y) = (b) fy(x, y) = (c) fax(x, y) = d) fxy(x, y) = f(x, y) =…

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Q: Let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 3, h'(1) = 4, g'(2) = 3, and f'(3) 7. Find r'(1) %3D…

A: Recall: The derivative of a composition is the product of the derivative of the outer function (…

Q: The weights of ice cream cartons are normally distributed with a mean weight of 11 ounces and a…

A: Given : μ=11 ounceσ=0.6 ounceX~N(μ=11,σ2=0.62)Let, for sample of size n,x¯~Nμx¯=μ,σx¯2=σn2

Q: If an object moves in the plane with a position r(t) = (x(t), y(t)) , then between times t = a and…

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Q: se the chain rule to compute and at (u, v) = (1, I) where f(x, y, z) = x²y + y²z + z²x and r(u, v) =…

A: Given: fx,y,z=x2y+y2z+z2xr→u,v=eucosv,eusinv,u2u,v=1,π4 To find: ∂f∘r→∂u=?∂f∘r→∂v=? Concept used:…

Q: find ∇f(x,y)

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Q: Consider the following graph of y = f(t) which is composed of line segments and semicircles: y =…

A: Here in the question, the graph of y=fx is given which is composed to the line segments and…

Q: 5. Let f(x, y) = sin(2.xy). Find f.(x,y) A) f,(x,y)= 2xcos(xy) B) f,(x,y) = 2y cos(xy) C) f.(x,y)= 2…

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