let Ant [F(点)] T=0 = 0, 1, 2, ver Prove that ① A.= F(U) 2 A₁ = U₁ F (uo) 4. (40) Uz ℗ A3 = U₁ F (40) + U₁ Us F (40)\",\ U ₁ F (U.) 2 〃 ④⑦A₂ = U₂ F(U01 + 2 + U, F(U). الراكب

Q: Construct a Formal Proof of validity: (Ǝx) Ux ⊃ (y)[(Uy v Vy) ⊃ Wy] (Ǝx) Ux • (Ǝx) Wx ∴(Ǝx) (Ux •…

A: Given that (Ǝx) Ux ⊃ (y)[(Uy v Vy) ⊃ Wy] This means there is x which satisfies the conditions. The…

Q: Q1) Find the canonical form of these question : a) f(x.y,z) =F=x' y' z+x y° z" +x y z b) f(x.y.z)…

A: We are given: f(x,y,z)=F=x'y''z+xy''z''+xyz We are given the standard Form. F=x'y''z+xy''z''+xyz…

Q: 1) Let f(z,y)- . Compute DS(z,y) where u- (4-9)

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Q: Q1] (A) If F(x+y-2₁x² + y²)=0 where z=2(x, y) and дz дz -у-=х-у ду ах - 0 then prov

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

Q: v : {p, q, r, s, t, u} formula (t → g)A (u → p) A (T → s) ^ (tAg → r)A (s t)^ (uAp + 1L) Find an…

A: Given that v:{p,q,r,s,t,u} to {0,1} It satisfies a formula, (t→q)∧(u→p)∧(T→s)∧(t∧q→r)∧(s→t)∧(u∧p→⊥)

Q: z = f(st - 3, s2 +t) and fi(-1,9) = 3, f2(-1,9) = 7, fu(-1,9) = f12(-1,9) = f21(-1,9) = f2(-1,9) =…

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Q: 4. (a) Prove, without recourse to geometry, that u • (v × w) = v • (w × u) = w • (u × v) = −u • (w ×…

A: Solution: To  solve  the  above  problem,  we  need  a  basic  result .Let  us  recall  that  first…

Q: Find V· (V × F), if F(x, y, z) = 3e**i+3xe'j – 3e²k. - V·(V × F)

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Q: If f(x) = xe* — 1 and the interval [0, 1] by using newton's method then x₂: =****** a) 0.571020 b)…

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Q: Prove f-1(E U F) = f-\(E) U f-1(F)

A: We have to prove that f−1E∪F=f−1E∪f−1F. Let x∈f−1E∪F hence, x∈f−1E∪F⇔fx∈E∪F…

Q: Find a function that satisfies the conditions f " (x)=x8, f'(0) = 13, f(0) = 10.

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Q: Q2) homeomorphism. Prove or disprove: The function f: (R, T1) - (R, 13) defined by f(x) = 3x is a…

A: Clearly the given function f(x)=3x is continuous. Now we want to check whether it is bijective,

Q: Let F(x) = S c²dc. Compute F'(t) = F(t).

A: The fundamental theorem of Calculus says: If F(x)=∫0xf(t) dt...(1) then  F'(x)=dFdx=ddx∫0xf(t)…

Q: sume that f(t) is continuous on [a, b| and that u = g(t) is cont ferentiable on [a, b], then f(u)…

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

Q: Let f(t) = 3t – 8t + 5e'. - Then f'(t) =

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Q: 1 Find af /dx, Əf / dy if ар лах а fax,y) - ху bfcxy)= exy cЈ fexiys - x cosx cosy d.j fexiyo=…

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Q: suppose that f (u, v) = ue", where u =rs and v =r + s. The composite function f(u, v) is equal to:…

A: A composite function is one which is made of other functions or in other words function values are…

Q: 2. Suppose that {f(t)} = F(s) with F a differentiable function and that {f(t)} exists. Then L{-te*…

A:

Q: What are the coordinates of C' after its preimage, C(5,-3), is reflected over the x-axis? O (5,3) O…

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Q: 1. Consider the matrices A₁ 4 = ( 1 ) - 1 3 0 A₂ 42 = (3-2) ₁ 4₁ = ( 2² -2²), , A3 0 -2 These…

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Q: Suppose f, g:C → C are differentiable. Prove that fg is differentiable and that (fg)' = f'g + fg'.

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Q: Suppose that f: R² → R² is a function such that f (1, 2) = the linear approximation. (Use syntax…

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Q: . Find, from first principles, f(2, -1) for f(x, y) = 2a?y³ + e2y. ,2,,3

A:

Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

Q: Let /: X →Y be a function, A, BC X and C, DCY. Show that: 1. f(AUB) = f(A) uf(B) 2. If AC B, then…

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Q: Assume that R (t) + 0. Show that T'(1) = R' (t) – (De||R (t)|)Ť(t) T'(t : ||T (t)||

A: As per the question (and the general conventions in vector calculus) we have a vector valued curve…

Q: The function f(x) = |ax - b| + c|x| : x in (-∞, ol where Find the

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Q: Let h(æ, y) = f(x)g(y) + (9(y))² and suppose that f(1) = 5, f'(1) = 3, g(2) = 8, g'(2) = 10. Then…

A: Given function is - h(x,y) = f(x) g(y) + g(y)2             ............................(1)We have to…

Q: 2(x-1) If y = Vx² – 2x then y' 3x2-2x

A: For the first part, we differentiate the given function y with respect to 'x' and use change rule of…

Q: Please take turns to work on the following questions: 1. Let f(x, y) = x² + 3xy + y² Compute (a) af…

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

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Q: Let z = f(st – 3, s? +t) and fi(-1,9) = 3, f2(-1,9) = 7, fu(-1,9) = f12(-1,9) = f21(-1,9) = f2(-1,9)…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

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: for 3x'z -x'y² +2z + 3xy = 0 ( Hint: Let %3D F(x,y,z) = 3x z - x'y? + 2z +3xy) %3D

A: Explanation of the answer is as follows

Q: Let R (s, t) = G (u (s, t) , v (s,t)) where G, u, and v are differentiable, и (1,2) — 5, из (1, 2) —…

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Q: Show that u(x,t)= f((x+a*t)+f(x-a*t))/2

A: Given PDE is utt=a2uxx subject to ux,0=fxutx,0=0 We know that the general solution of the PDE is…