Let E = Q(V2,v3,V5). (1) Find 3 distinct non-trivial elements in Aut(E/Q). (2) Denote such three by o, t, 8. Find Eo, Et , ES, AND E{o, t}, E{o, 8}, E{t, 6}, E{o, T, 6}.

Q: Find g(u(х, у, г), в(х, у, г), и(х, у, 2)) if g(x, y, z) = z sin xy, u(x, y, z) = x²z", v(x, y, 2) =…

A: Given:  (1) gx, y, z=zsinxy (2) ux, y, z=x2z3 (3) vx,y,z=πxyz (4) wx,y,z=xyz To find : gux, y,z, vx,…

Q: Let w = r = uv, s = u – 2v. Use appropriate forms of the p2+ s2" dw dw and du chain rule to find in…

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Q: 4. Evaluate fe fds where f(r, y, z) , ) and 0 <t< 1. = 12r2 and the path C is given by r(t)

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Q: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by f X,Y (x, y) = (x+y)/21…

A: The given joint pmf of X and Y can be described as X.       Y 1 2 P(X = x) 1 2/21 3/21 5/21 2…

Q: 12 3. If u lx + my, v = mx-ly, show that ди 4 + m

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Q: Suppose that w = f(r, s, t), where r = r(x, y), s = s(r, y), and t = t(x, y). Which of the following…

A: Solution is given below:

Q: 6. Prove that for x > -1 then Vn E N, (1 + x)" >1+ nx .

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Q: Let E={(r,0,z) : os es T, OS zs 1, 5Vzs rs 5. Compute

A: Introduction: The triple integral ∫∫∫Ef(x,y,z)dV with the region E=(x,y,z):a≤x≤b, c≤y≤d, e≤z≤f can…

Q: Suppose w = 6xy + In(4 + z²) , x = - , Y 3u + 9v, z = cos(8u). Find dw/dv when u = -5, v = -6. dv…

A: *to find:- Partial derivative of w with respect to v, when u = -5 &amp; v = -6

Q: Q2- By using Chain Rule, find əu/əx, əu/əy, du/əz at (x, y, z) = (√√3, 2, 1) U= p-q q-r p= x+y+z )…

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Q: Let X₁, X₂,..., X be a r.s. from N(,0) and Y₁, Y₂...., be another independent r.s. from m…

A: Solution

Q: Given u(x, t) = t-²e¯, 2 , compute:

A: We can find the required answer as below.

Q: Suppose that x̅ = 12, Sx = 2, and z is 1. what is X?

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Q: Exercise 4 Show that for cach k EN it holds that kn-k < n! S n", Vn E N, n2 k. Deduce from this that…

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Q: Let f(x, y, z) = x³e" Vz² + 5 and let x = rt², y = r2t², and z = sin(t) cos(r). (a) Draw a tree…

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Q: Prove that if a e R, then a 0 = 0 = 0 · a. Suppose x, y, z E R. Show that xz = yz if and only if…

A: We will prove the given statements.

Q: Let w = r = Uv, s = u - 3v. Use appropriate forms of the + s²' dw dw chain rule to find and in terms…

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Q: 0/ the Valke of & that makes the Velteof the fumetion 2.

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Q: 2) Let u(xy,2) = でさす。R。 () Find He(tいり, "g(1,0,り、 Uy(1,0,1). ニ0. (k) Show that oty a22

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Q: 비 az and Given that z = e*, x= 2u+ v, y= .y==. Find using the chain rule. au

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Q: Sw 1. Given w = xysin( z?), x =s-t, y = s2, z = t2. Use the Chain Rule to find St

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Q: locally Lipschitz in (t,x)E[a, b]x D.

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Q: The Wronskian of y,(t)=e 2, y,()=e" is-e St. Select one: True False

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Q: (b) Find fx, fy and f,if f(x,y,z) = zln(x²ycosz). (c) Use chain rule to find du and 2 if z =;x =…

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Q: Queston #o 4 Show that X, Ixe, where x, and Xe E IR X= (1,1,1, -1) Xz = (4,2,2, -1) %3D

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Q: az Find if yz – In z = x + y ax

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Q: Suppose that w = f(z,y, z), z = h(s), y = g(s, t), z= k(s,t) and all the conditions required for the…

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Q: 3. If Rw (T) is the autocorrelation of a white noise w(t) and S e-217| Rw(t)dt = 1, find Sw(f).

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Q: If Σa, is divergent and Eb, is divergent, then Z(a + b) is divergent.

A: The given statement is false as sum of two divergent series may converge. We illustrate this as…

Q: Find (T3 • T, o T1)-1 if Ti 1(х, у, 2) %3D (х - у, — у, х+2) T."(х, у, 2) %3D (х -у+z, 0, 3x) T(х,…

A: This question is related to linear transformation . See 2nd step.

Q: 4. Let f(x, y, z) = x²y+ y² z. Use the Chain Rule to calculate ðf/ðs and df/ðt (in terms of s and t)…

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Q: Find e² in the form of u + jv and le²| for z = 2 + 3nj

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Q: let z- 5 dy By chain Ruie

A: Given z = √x dy/dx = (1/2√x)•(dy/dz) We have to find d2y/dx2 .

Q: 1. Let P, X,Q denote distinct points of E. If X is between Pand Q, show that d(P,X) d(X,Q) 1-t, for…

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

Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: 1. Let s, =2+j8 md -, = 4+j36. Show that a. -1+- = -+- 1 -1- -2 -1 -2 = -1-2 -1 : b. C d. =2 ||

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Q: Use the Chain Rule to find ôz/əs and əz/ðt. z = tan(u/v), u = 4s + 7t, v = 7s – 4t Əz as az II

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Q: ☺ RB=R defuid by T☺)- matria "A" it. T@)- A:). つレ- TV4 Let T: -3v-Jw ). Füd

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Q: Q2- By using Chain Rule, find au/ax, du/dy, du/az at (x, y, z)=(√√3, 2, 1) u= p-q 9-r' p = x+y+z…

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Q: For the following PMFS X and Y for k e {0,1,2,3, ..] Px (k) = { %3D otherwise for k e {0,1,2,3, ...}…

A: From the given information, PXk=e-λλkk!, k=0,1,2,3,....PYk=e-λλkk!, k=0,1,2,3,.... If λ=1, a) The…

Q: 22. (a) Prove that [0, x] = [0, y] for all x, y E Z, x + 0, y # 0. (b) Prove that [ax, ay] = [x, y]…

A: (a) we have to prove that  0, x = 0, y for all x, y∈Z, x≠ 0, y≠0 proof as x, y∈Z, x≠ 0, y≠0 Z is the…

Q: Let V =(1,2,3,4),V=(0,2,t,3) and w=(!,!,,1) 1. Find t so that u t v and w are to each other. or…

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Q: Assume that z = ƒ(w), w = g(x, y), x = 2r^3 - s2, and y = re^s. If g x(2, 1) = -3, g y(2, 1) = 2,…

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Q: In GL(2, Z,,). det

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Q: Let z = √7xy +9y, and x = s³ and y = 1². Use Chain Rule to find dz when t = 1 and s = 2.

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Q: Compute I ds over the path C : F(t) = (t, 2t,ť²) from (0,0,0) to (4, 4, 4).

A: The answer is given below:

Q: If f(x,y,z)=z In(x²ycosz), then fz is O 2z X OZ y O2z y O In(x²ycosz) - ztanz <|N

A: This question is related to partial differentiation, We will solve it using given information.

Q: Suppose z = f(x,y) where x = Puv and y=u+tv². Given that z,(4,3) = 4 and z,(4,3) = – 1. Compute z,…

A: Explanation of the answer is as follows

Q: 4: a) Let X.X., X -N (Hi,6f). Let Y,, Y2 Ym-N (u2,63). .... d (1-a) % CIfor oi when ai. a known.

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