) Let u be a function of R² such that ди ди (x, y) | Әх = en prove that ду (x, y); for all (x, y) ∈ R2 ди ди u(x, y) - u(y, x) = (x - y) ax (x*, y*) +(y-x) + (x,y') Әх ду

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A: Given: Tx,y→x+2, y To determine: T2x,y→?,?

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A: The given function is: y =  f(x) (2, -3) is a point on the given graph.

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A: (.)  Leibniz rule :      Given ,(A).        where   and   .

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Q: 人 そはっけ)ことス,ソフ ク=ム Cうk CurlF 支ド = 22 ズ 0y a2 %3D -> (-出)5+ (号-)k !! よいF (ス)+ C)+塩(の)こ2 ニ Find a…

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

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A: Note: The correct option is not in the option.

Q: [} [2] » 21. Let u = and v = Show that is in k Span {u, v} for all h and k.

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Q: rch Rank Page Order 172 5 C (c) u" (t) +8u' (t)+32u(t) = 32 (d) 4u"(t) + 12u' (t) +8u(t) = 8 (e) u'…

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Q: of af and Let f(x, y, A) = xy + A(5 – x – y). Find· ax' əy` af

A: f(x,y,λ)=xy+5λ-λx-λy .....(1) Differentiating (1) partially with respect to x, ∂f∂x=(1)y+0-λ-0…

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A: We have to find functional value.

Q: 1 1 T+ 2 1 B T+ - T(2)"-1 3(T, T)

A: To prove  βT+12,T+12=πT24T-11βT,T It is known that  βm,n=ΓmΓnΓm+n Now, for m=n=T+12,…

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Q: af of H.W: Find and for the functions: b əx ду 1. f(x, y) = (xy-1)² 3. f(x, y) = (x²-1)(y + 2)…

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Q: Let a be a real number and f(x, y) = 5ax?y+ 5xy³. Let v = 3i – j and let Vf(x, y) denote the…

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Q: • The Doman of f(x) = 4 – Vx is 1. (2, 0) 2. [-2,0) 3. [2, 00) 4. [-2,2]

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Q: ~ on T by (x1, y1, Z1) Let T 3D {(x, у, г) € R'| (х, у, 2) # (0, 0, 0)}. Define ~ on T by (х1, У1,…

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: (9) Ur = = UF'(A)) and that f Prove that f-1 (μη) = - U ΜΑ»). ΑΕΛ

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Q: If f(x, y) = (2x? + 8y²)í, then f_(0, 0) = %3D A) 0 В) 1 C) 4 D) 2 E) Does not exist

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Q: Let f be a function with continuous second derivatives, defined by: z = f (xy, x² + y") If we take u…

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Q: Let u and v be defined implicitly as functions of x and y by the equations xv + yu 5 x² – y3 + uv² =…

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Q: show the function is continous dis continou or 2=(2x+3 3メ→1」Xハz F(x)ニ

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let W(s, t) = F(u(s, t), v(s, t)) where u(1,0) = -2, u, (1, 0) = 8, ut(1,0) = -4 v(1,0) = -3, v.…

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Q: If (x* – y*,x – z°) = 0,z = z(x, y), prove: az y3 az +x³z4 ax - %3D ду 3

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Q: 3- Give the solution of Poissois equation マu- fcx,g) ミn e = h(x, y) in terms of corres ponding…

A: Given Poisson's equation : ∇2u=fx,y               in Ω∂u∂n=hx,y              on ∂Ω=Γ Apply Green's…

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A: We have to show Note: In the question  is given which is incorrect. It should be

Q: z} 0,1} definition for f: X→ A that is a well-de- (0, w), (-1, w), (-2, w)} , (0, w), (-1, w), (-1,…

A: We have to choose the correct option from the given options according to the given information