pour x20 a) Find density of z. (X4) et give ils diskribulion function Fla). b) Y: 2-X , use two diflecont melhads lo find the mean and the vorance of Y. l Explain the effect of transforations af Z: H, (X) et Y- H, (X)

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Q: the function is a metric of R: d(x,y) = sqrt(x^2−y^2);  x,y ∈ R

A: let z1=(x1,y1) and z2=(x2,y2) now, d(X x Y, d) is a metric space if 1)d(z1,z2)=0 if z1=z2 now, if…

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Q: Q1: Find the tangent plane and normal line of the surface F(x,y,z)=x² + n + y² + z² = 10 at point…

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A: Topic:- vector algebra

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Q: 6. Tangent Plane dro find an equatin the Plane and a set Line equatin g tho of Tangent * 9 o the…

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Q: [15] (2) Consider the function ƒ: R² → R, ƒ(x, y) = x² − 2xy + 2y² Determine Vf. a) b) c) GIVEN: The…

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Q: Consider the directional derivative of the general function z =, = f(x,y). a) Where is it a i)…

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Q: Q2) Evaluate ff xy dA Over the region enclosed between y=x, y = vx and x = 2, x = 4

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Q: Q3A) Find normal line and parallel plane to the function f(x, y, z) = x²y²z² - 4 At point (1,-1,2).

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Q: Q5/ Find the moment of inertia about the x-axis of a thin plate of density 8 = 1 bounded by the…

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Q: Q4) Consider the function f(x,y,z) = x³ – xy² – zy a) Find the derivative of f(x, y, z) in the…

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Q: 3. Determine the equation of the tangent plane and normal line to 2xz + y²z³ = x + 5 at (1,0,3)

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Q: Example: find the tangent plane and normal line of the surface f(x, y, z) = x + y' +z-9=0 at the…

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Q: Let W= Span(u) where u = find the distance from y to W V13 b) V3 13

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Q: If F(x, y, z) = z - f(x, y) and s is the graph of z = f(x, y) and (a, b,c) is a point on the surface…

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Q: Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find ∂z/∂t.

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Q: d (x, y) = (x - y)^2 does the function define a metric o

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