QI: Prove that vM ror VM 2 s where r and s are the positive integers unless M # r .

Q: Evaluate the integral (2 + 6) (2? + 6z + 2)*dz by making the substitution u = x² + 6x + 2. + C

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Q: Q3: Prove that Σ(y₁ - y) = 0 AND Σfi(y₁ - y) = 0

A: The question is about proving given equation. To prove : ∑ ( yi - y¯ ) = 0∑ fi ( yi - y¯ ) = 0

Q: QR MN ZN = ZR QS MP RS Given: NP Prove: R N

A: In △MNP and △QRS QRMN=RSNP=QSMP

Q: Q1: Prové by induction nzZ! ☆ (1- 1 htI ( Here JJ (Pi") stande for froduct) means (I- I

A: A detailed solution is given below.

Q: TQ residue of f(z) = e (z – 1) (z + 9) at z = -9 is 10e-9 :Select one True False

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Q: Q: Show that the functi on f:R →R given by f (x) = ax +b, where ab e R, a #0 is a bijection.

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Q: 10e dz by residue theorem, where C is the contour |2| = 2 Je 1z4 +5z3 Evaluate

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Q: Complete the proof that ZYXZ SUT. P Q R. U W Y

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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: 1 Using Convolution theorem, find (i) L (s+a)(s+b),

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Q: R Given: VS = TR and ZTRS = VSR Prove: ARST = ASRV

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Q: Q53- X--) (xij-Xi - X.j+X)=Zero 13D 「に )に prove that e to

A: We need to prove the given equation.

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

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

Q: af Given f(x, y) = In(6x² + 8y²) then %3D

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Q: 2. Find the correct value of c such that P (Z < c) = 0.4. %3D C =

A: According to the provided information, P(Z&lt;c) = 0.4

Q: Prove this! P (an) = W/ NM) [M-N (p-q)" ] 8 Npq %3D exp

A: your question is not clear i think some error in the question plz confirm it.....

Q: (b) Let X = {A E Mat2(R) : A is upper triangular} and let Y = {A € Mat2(R) : A is lower triangular}.…

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Q: For z C, show that the solutions of cosh(z) = 1 are z= i2km, for ke Z.

A: We need to prove that the solutions of the equation: cosh(z)=1 are z=i2kπ, where z∈ℂ, k∈ℤ.

Q: Prove that in the pairs of positive numbers ¤, y for æ² + y° = r the sum a+y is greatest when z = y.…

A: Here we solve the given problem of calculus.

Q: EX: Verify that z= I+ V3i satis fies the 2. eq.

A: the given equation is z2-z+1=0 given the value of z is z=1+3i2 substitute the value of z in the…

Q: Q111f и %3D (1 —2ху + у?)""/2, Prove that: ди ди y əx y? u3 У ду

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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: %3D then przove that .cūxR=0 and vxcãuFR)= 2Ù

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Q: 2. Given: KM bisects ZJKL. Prove: m22 = m23 %3D K M 3.

A: Concept- Opposite angle are same

Q: suppore that f(x.v,Z) = x*y +x2 and x cu,v) = sincu)t(os (u) Y(u, v) = Sincu) - (oslW find of oflav…

A: Given: f(x,y,z)=x2y+xzx(u,v)=sinu+cosuy(u,v)=sinu-cosu To determine: ∂f∂u,∂f∂v

Q: graup Consider a dibedral 2. Du= carb: d=b-(ab)"%=D1> Discuss all passible Commulators 'and verify…

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Q: 4. a) Prove that i) V=I ii) fx+nh = ! I+A 1+A (1) AK fx. = 4k=0

A: Introduction: In numerical analysis, there are many different operators that are used. These…

Q: Prove that c?p?-(jx² + jy²+jz³) is the invariant quantity equal to c?po?.

A: Consider the provided question,   Prove that c2ρ2-jx2+jy2+jz2 is the invariant quantity equal to…

Q: Q3: A. Find Wer if W = f(x, y) {x = reost, y = rsint W₁,

A: From chain rule we know if w=f(x,y) and x=g(r,t) and y=h(r,t) then, ∂w∂r=∂w∂x∂x∂r+∂w∂y∂y∂r

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

A: See the attachment

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: Q: If u =f(x² +2yz, y² + 2=x)Prove that (y-ax

A: Step by step compute the derivative with respect to each variable x,y or z. Then substitute it in…

Q: Q(x) = √3/2+² Ser fet de Prove that & QQ (-∞ ) = 1

A: Here we can use Gamma function formula Γn = ∫0∞ xn-1 e-x dx to evaluate the given improper integral.…

Q: T. Given ;XTE KR ZWST Prove : SR Il TW.

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Q: Q- show that yo+(?) sy + (2) B²y_₁ = y + (1) DY...+ (1²¹) Ay -

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Q: c. Use De Moivre's theorem to find the following: 4 i. [1+ v3i]*

A: Dear learner, As per our guidelines, we can provide the solution for first one only. Kindly post…

Q: zez Use Cauchy residue theorem to evaluate . (z'el + ) dz, C: 4x? + y2 = 16. %3D

A: We know that  z2e1πz is analytic throughout the complex plane. Hence by Cauchy's theorem ∮z2e1πzdz=0…

Q: a the diagram, PU||QT, Ì = 42°, RQS = 82°, = v, UPT =r and QPT = x+40°. Prove that PT|QS. %3D P…

A: Given: PU||QT Concept: Pair of interior angles on the same side of the transversal are supplementary

Q: (c) Evaluate d Gosh: where C: |z| = 2 by using Cauchy's residue theorem.

A: Given integral is ∮C dzcoshz;   C : z=2 As, we know  If z = x+ iy then z =x2+y2 As given that  z=2…

Q: SU SW. Complete the proof that ASTW ASXU. T. V W Statement ZW ZU SU N SW ZS ZS 4 ASTW ASXU 2.

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Q: DX Cecelia wanted to prove that in the figure. She krows that RD TB %3D Select all of the statements…

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Q: 2. Use the met hod of undet er mined coefficients to solve t he syst em x' = Ax+f, where - -] b. A =…

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Q: b) u(х, у) on the domain 0 < [z| < ∞. x² + y? Why is v(x, y) single-valued in b?

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Q: V- Assuming Cov(X, u) = 0 allows us to equate Ex û to zero. True or False? Explain.

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Q: of the following conditions imply that B = se, either prove or give a counterexample. B] AUB = AUC…

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Q: Find T, N, B, K and t for r(t) = ti +÷e2'j when t = In 2. 2

A: answer is in next step

Q: uppose that X~N(µ, o²) and that P(X 3.6) = 0.6554, what are the alues of u and o?

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Q: State De Moivre's theorem and if z 7+ j4, find z5 using the ( theorem.

A: Given query is to find the value of z5 using De Moivre's theorem.

Q: Which condition would prove AJKL - AXYZ? K Y 56 7. JL XZ 造=8 KL 8 JK %3D XY

A: We have to find which condition would prove ∆JKL~∆XYZ.