[D²,2²] = 2(2&D + î) 2(2£D + î) Prove that

Q: %3D 2. Prove that -24y of 3. =2x

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Q: 5. Prove that So*(y – 0)dydr =

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Q: Show that the function a Y1 (x, y) = [21 2] в с Y2 is an inner product on R? if and only if b2 – ac…

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Q: 5. (6 + 15i ) 3

A: this is a problem of complex analysis.

Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y+ z + w= 6 .…

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Q: Suppose f(x, y) = x² + 2æy+ y². Which field plot is Vf? Justify your answer. 鹿

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Q: B = and C: .Prove that A = B² =C? = 1. 3. Given A = %3D

A: Given: A=0110, B=0-ii0, C=100-1 We know that for a 2×2 matrixP=abcd, P2 is given by…

Q: "he pmf of X is 4.x – 1 - fx(x) = where x = 1, 2, 3 %3D %3D to

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Q: Prove in detail that Q(/3+ v7) = Q(V3, v7) %3D

A: According to guidelines we solve one question.

Q: Solve using Cramer's rule. 2x+8y = 11 4x+6y = 3 %3D %3D

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Q: verify that (A + B)T = AT + BT

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Q: Use Fermat's Theorem in your proof that Vn E Z>², 2 is irrational. I

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Q: Prove that c = cn. i=1

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Q: Show and use d(Xn, FCN))<« d(Xn-1 'x) Vny? To prove X = fx) %3D

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Q: Find all positive integers x, y, z satisfying x · y · z² = 5xyz. '*

A: Introduction :Given , positive integers x,y,zwe have asked to find the values of x,y,z which…

Q: Prove that + J2 (x) + J, (x) = 0

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Q: Solve the folowing equation on [0,2pi) 2sqrt2 +4cosx=0

A: In the given equation, the cosine function is the trigonometric function:   Rewrite the given…

Q: 1-a*** a zi i. La 1-a

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Q: b) g(x) = S,* In(2r + 1)dr

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Q: 5. What is UF, where F = 0? Prove the correctness of your %3D answer / computation.

A: To find- What is ∪F, where F = ∅? Prove the correctness of your answer/computation.

Q: 2. (– 13 + 3i)31

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Q: Prove that d (sec"x)= 1.

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Q: %3D n-0o 2n

A: Given. We are given a limit and we need to prove that the limit of the given function at infinity…

Q: if x, y>o such that x Sy then Vã svy Prove by direct method

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Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y + z+ w= 6 3x…

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Q: prove that two vectur ae orthognal A = x + 4y+32 B =4x+2y-42

A: See the attachment

Q: F(p), then prove that

A: simple use of integral transformation

Q: Show that Z, dv=2010 %3D if B= 2) : -1 Śn s3, ISySY,e

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Q: Evaluate z'dz where C is z=2 by Residue theorem. (z-1) (z-3) (s-2) ,(1-2)}

A: Given A complex integral we can use cauchy's residue theorem to solve the problem

Q: 103 Let = 2+j"8 and z, = 4+ j06. Show that a. + =2 = =, +z2 b. 1- 2 = =-2 с. d.

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Q: Q3/A/ Prove that ) + ",) = C). %3D إضافة ملف

A: As per our guideline we are allowed to do 1 question at a time. I think you hav already done 2…

Q: LZHP - DTNV. Complete the statement below. ZZ = _2_

A: Consider the following condition: LZHP~DTNV Hence, ∠L≅∠D∠Z≅∠T∠H≅∠N∠P≅∠V

Q: Prove that jer² √ d dx = 2

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Q: Calculate A and B so that t B %3D 1+1 (1-z²)

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Q: If Z=1//2+j/v2 then the value * ?=of conjugate of Z^5

A: According to Euler, the complex number of the form cosθ+isinθ can be written as eiθ. The conjugate…

Q: 3. Prove F (Vr)(A→ B) → (Vx)A → (Vx)B. ->

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Q: Consider P2 with the inner product = f (x)g(x) dr. Then d(x, 2) Jo

A: d(x,2) represents distance between the vectors x and 2 P2 is the set of all polynomials with degree…

Q: Use Cramer's rule to solve for z. Зх — 4у + z %3D 3 2х + 3у = 8 5y + 8z = 11

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Q: dv Prove that 4u/2n

A: We use Gamma function to prove the given result.

Q: Find the cemplex fourth routs of Z: 2 J3-22

A: Given, z= 2√3-2i Therefore, r= √[(2√3)²+(2)²] r= √(12+4) r= 4 θ= tan-1(-2/2√3) θ= -30°

Q: Z-1 %3D ,then prove that x2 + y? = (x-1)2+y2 (x+1)2 +y2 (1) If Z %3D Z+1

A: Topic- complex number Note:- as per our guideline if more than one question uploaded than only first…

Q: (a) Prove that if f e C (R²) then a (af af %3D

A: This is a problem of the calculus of several variables, higher dimensional calculus.

Q: on vectors for t2 0.

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Q: B a. In the figure, if AX = (3x + 1) cm, BX = 4x - 1 cm, AY = 4x + cm, YC= 5x-1 cm and x = 2, prove…

A: SOLUTION-

Q: Solve for z using cramer's rule.  2x-y-z=4 4x+y+z=2 3y+z=2

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Q: Use Gramer's Rule to Find K,y and Z -y-22 = -8 %3D + 32 = 2 %3D 7X +y+Z = 0

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: I. Solve using De Moivre's Theorem. Given that z is not real number and z = 1, show that w = z-1 z+1

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