Xx 0 1/6 1/6 1/6 1/6 1/6 0 0 Find Var(X), Var(Y), and the covariance and correlation of (X,Y). Determine Var(X + Y). Are X and Y independent? Comment on the relation between Var(X) + Var(Y) and Var(X + Y). 1 1/6 2

Q: Find fx (x,y), fxy(xX,y), fyx(x,y), and fyy (x,y) for the following function. f(x.y) 2x'y +5x° +9y…

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Q: For the function f(x,y) = xexy, find fx and 1 fy. fx= 0

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Q: The range of f(x, y) = – Vx2 + y? is %3D Select one: a. R? x b. [0,00) C. (- 00,0] |

A: We have to find the range of fx,y=-x2+y2 .

Q: Find V²f by the formula V²ƒ =div(grad f) given f(x,y, z) = e³wyz grad f = [| V²f =

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Q: 1. Let u = PQ and v = PR, where P = (2, –1,3), Q = (0,5, 1), and R = (5,5, %3D (a) u v (b) The angle…

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Q: If f(r, y) = 3y? - 6xy + 11a, then is given by: O 12 O 6 O -5

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Q: For the function f(x,y,z) = In (7x+ 2y +5z), find fy, fy, and f,. fx =口

A: Given,           fx,y,z=ln7x+2y+5z

Q: Given f(x, y) = 4x° – 4xy? + 5y°, find -

A: Find out fxx(x,y) and find fxy(x,y)

Q: r) Λ (q r) Ξ (p V q) Determine whether (p r

A: Construct the truth table for p, q and r. use p and r to find the p →r.

Q: Find f, and f, for f(x, y) = 12(6x-3y +8)°. %3D 1,(x.y) = %3D

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Q: 4. Evaluate both sides of Green's theorem, for: F = (-x²y,xy²) where C is shown in the following…

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Q: Prove that : V.(V×A)=0

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Q: Given f(x, y) = 2x² + 6xy³ + 4y5, find the following numerical values: f(3, 3) = 4. f₂(3, 3) =

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Q: If f(x, y2) = x2 + y² + Vxy find: and (x?y) ду af(x²y) ax

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Q: Given that J(9, -4), K(6, -10), L(1, -1), and M(x, 4), find the value of x so that JK LIM.

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Q: Given r(t) = ⟨t, t2, t3⟩, find v(t) and a(t).

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Q: xa, ya, + za Let A = (x² + y? + )3/2 i show that V X A = 0.

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Q: Is the following statement true or false? Explain your answer. {(x, y) E R?:x? -x = 0} ((x,y) E R?:x…

A: Let consider two sets A & B such that A: { (x,y) t R2 : x2 -x = 0}and B : { (x,y) tR2 : x-1=0}

Q: Find V. (Fx G), if F(x, y, z) = 4xi+j+13yk and G(x, y, z) = xi + yj – zk. V. (Fx G) =

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Q: If v = 3i - 6j and w = i + j, find (v . w)w.

A: Given:          v=3i-6jw=i+j Using the component formula for the dot product of two-dimensional…

Q: Find the value of zo so that dz = -2ni Pst-12 (= – z0) (z – 14i) |

A: Given ∮|z|=12z(z-z0)(z-14i)dz = -2πi

Q: if Find X and y f (x+3,y)=(6,-24-9).

A: An ordered pair is equal if the corresponding elements are equal. Therefore x+3 = 6x+3-3 = 6-3x = 3

Q: Find: Ex, fxx , fy, fyy, fxy, Fyx x +y F(X, y) = X+y x4-1

A: Given that: f(x, y)=x+yxy-1

Q: ry? Find I.A. -dA, R= [0, 4] × [ – 1, 1] г? + 1

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Q: If it was p(x, y, z) = /x² + y2 + z? find V ?+

A: The formula for ∇2ϕ=∂2ϕ∂x2+∂2ϕ∂y2+∂2ϕ∂z2