Suppose T(x,y) = (2x, 2y) and U(x,y) = (x, -y). Is T∘U=U∘T?  Justify your answer.

Q: Find ∂y/∂x1 and ∂y/x2

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Q: Find f, (x.y) and f, (x,y). Then, find f, (1,-3) and f,(-1,- 2). f(x,y) = - 5xy + 2y +6

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Q: ?w Əv у Find when u = 0, v=0 if w=x² + ₁ x=6u-2v + 1₁ y=u+4v - 1.

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Q: If f(x, y): X 2y + 1 use the definition to find af (x, y) ду

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Q: Find f, (2,0) if f(x,y) = 18x e Y. 1,(2.0) = %3D

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Q: Suppose that f(z, y) = 10z²y² + 8z? + 2y? then find the discriminant of f.

A: We have to find the discriminant of the function of two variables fx, y. It is given that the…

Q: Let f(x, y, z) = x³ + 5x²yz + 3xz+ 3, v = Then: D, f(a) = 201 0 -2 and a = -5 2 -5

A: Given that f(x, y, z) =x3 +5x2 y z +3xz+3 The directional derivative is a concept from multivariable…

Q: Evaluate |(a,b)=(0,0) given that f(x, y) = 3x² + [y]; x = e²a+b₁ e²a+b; y = a² + t² + 1 да

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Q: Let ā = (1, 3,-1) and b (-1,0, 2). What is the y-component of ā x b %3D %3D 1 -1 3.

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Q: f(x, y) = 3x³ – 2x² y + 5xy + 7y + 14 - Evaluate: %3D dxôy О а. -6х O b. 10y – 4x О с. 0 d. 9x + 7y

A: Given problem:-

Q: Translate Q (0, -8) using (x, y) → (x - 3, y+ 2). Your answer: O Q'(-2, 5) Q' (3, - 10) O Q'(-3, -6)…

A: The transformation is, (x,y) ------> (x-3, y+2) So, (0, -8) ------> (0-3, -8+2)

Q: Determine if F = x²yî + (xyz +29)ĵ – x²y²k is conservative or not %3D

A: For vector field F⇀=ui^+vj^+wk^ Curl(F)=i^j^k^∂∂x∂∂y∂∂zuvw   For vector field F⇀ to be conservative…

Q: Let g(x, y) = 3.2³-6-2²-5.y2 +1. a. ag Show/hide

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Q: If u = (u, uz) and v = (V1, V2), how do you find u + v?

A: Given: u=(u1,u2)v=(v1,v2)

Q: For two points (x1, y1) and  (x2, y2) such that xi > 0, yi > 0 for i = 1, 2, we say  (x2,…

A: There are about 4 functions provided.To show:They are Schur convex or not.Concept used:i) Any…

Q: Find fy (-1,-4,-2) if f(x, y, z) = x³ z4 + 2xy – y? z + 1.

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Q: Q/ Let x~P(m) and let y = 5x , find the p.d.f of y

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Q: Y = -2X, then p(X, Y) = 1?

A: Solution

Q: If i = xi+yi+zk then grad (r") is equal to

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Q: For the function z = - 8x³ - 2y² - 2xy, find a z(1,-2), andz(1,-2). dz dz a ax' dy ax

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Q: If B = x°ya, + (2x + y)a, – (y – 2)a, find (a) V B (b) V X B (c) V (V B) (d) V x V X B

A: Given : B=x2yax +(2x2+y)ay - (y-z)az

Q: Q/ Let X be the r.v such that E(X) = 2, E(X²)= 2a , E((2+aX)²) = 2a3 Find the value of a. %3D %3D

A: Let X be the random variable such that, E(X)=2, E(X2)=2a, E((2+aX)2)=2a3

Q: Lemma*: If z(x, y) = W+H, then xZx + y2y = (xWx+yWy) + (xHx + yHy).

A: Solution: