Evaluate z*+3 olz-22²+1+e"]dz, te, C: |z-i-1|=2, CCW.

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Q: If =x+3y-z,=4xyz, w=22 -xy evabuate d(u, v,w)/ (, 2). at (1-,0).

A: We have to first find all partial derivatives.

Q: Discuss the Singulazities and Poles of fiz) = zéSinz (z-2) (zこいこょうと+ら)(2t (こか) +4

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A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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A: The answer is given as follows :

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A: Given that, ut=kuxx , 0<x<L, t>0u0, t=uL,t=0ux, 0=xL-x This is  the heat conduction problem…

Q: Let Z, = 2 cis 30° = 3elli %3D Z = In (1 + i) %3D If Z = Z,Z, + Z, Find Z].

A: From the given information. Write the complex numbers Z1, Z2 and Z3.

Q: Let Z, = 2 cis 30° Z2 = 3elli %3D Z = In (1 + i) If Z = Z,Z, +Z3 Find IZ.

A: First we convert all expression into a+ib form then make necessary calculation.

Q: 8. Chords AC and DE intersect at Point R in OQ. If AR = 6, RC = 7, and DR = 3, what is RE? %3D %3D

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Q: Suppose csc(4) =2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII

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Q: Show that |1 - (x, + x,) - (x, + x,) X,*z = (x, – ,) (x, – y2) (x2- ,)(x2 - 2) 1 -(), + x2) 1 - (y,+…

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Q: 2), Compute SE. di where Fュく-,) C is s shown

A: The general form of a vector valued function in three dimensions is given by F→=F1,F2, where F1 and…

Q: defined by ф Kerф %3D (1,-1] Kerø = {i,-i} Kero = {i,1} Kerф %3D (1,-1,1, -)

A: Option (d) is correct.

Q: Prove that: sec a + sec(120° +a)sec(120° – a) = –3 sec 3a

A: To prove that  secα+sec(120∘+α)sec(120∘-α)=-3sec3α

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Q: et X~U([-, 1) and let y = tan(r), show that y Cauchy(0, 1)

A: # using Jacobian transformation we have proved that y=tanx follow Cauchy distribution (0, 1)

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Q: (6) If u, =*-!P«(x)Pn -1(x) dx, show that nu, + (n – 1)n-1 = 2, %3D and hence evaluate u„.

A: Given un=∫-11x-1PnxPn-1xdx

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Q: If x,y,z are real numbers satisfying the equation 25 (9x* +y° )+9z²-15(5xy+yz+ 3zx )=0 then prove…

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Q: Exercise.2 Prove that cos-1 z =- In(z ± Vz? – 1)

A: The given problem is to prove the given inverse complex trigonometric identity. cos-1(z)=1/j…

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A: Given problem:- In R³, the point (1, 1, 1) does not belong to the cylinder x² + y² = 2.  True  False

Q: Ai How could you prove ZC AB ZCDB? Drag tiles to the empty boxes to correctly complete the proof.…

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Q: Show using MGF technique that if Z, - N(0,1), for i = 1,2,3,4,5 , then U = Ez - x² with 5 degrees of…

A: Using the MGF technique we have to prove that : U = ∑i=15Z2i ~ χ2 with 5 degrees of freedom, If Zi ~…

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Q: 1- -Н(y)-Н(yх) Prove that 2- H(x,y) = H(y) + H(x\y) 3- H(x,y) = H(x) + H(y}x) 4- Н(х., у) %3DН(х) +…

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Q: If x<y, prove that x<(x+y)/2<y?

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Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y3…

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Q: dual of c, is isometric to l'.

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Q: •1-i Evaluate 4z dz . J3i

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Q: matrisinin özdeğerleri aşağıdakilerden hangisidir? o {,-3} po {0,1} 9o {2,-글} {2, –}} d) o {2, –2}…

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Q: 7 cos(z) Driented ris countercleckwise ortented rectangle with -2-i , 2-i, 2té, -2ti

A: Contour integration

Q: Ju 20²u c² of2 (r, t) = u(x,0) = 0, ut(x,0) = 0 u(0,t) = 0 u(1,t) = 0. da2(x, t) + XX , 00,

A: Introduction: The basic method to solve a partial differential equation is the method of separation…

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A: 25. The given differential equation is                                     y1+1x+cos ydx+x+log x-x…

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A: We have to find out P2(x) and P4(x) by recurrence relation. We know that the generating function…

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A: True.

Q: prove in words: If {X, Y, Z} ` A ∧ ¬A, then {Y, Z} ` ¬X ` = derivability

A: Use the deduction theorem: Deduction theorem states that, If ┌ A⊦B then ┌⊦ A→B

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Q: Derive pz, 192. sjt9z, Hz(t), ez, čr: directly , if X ~ U (0, w) with r = 20, n = 30, w = 100. %3D

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

Q: Question #30

A: Note: Some of the basic calculations are directly written due to the question being very lengthy. We…

Q: docs google.com 10- [P+1(7) – P1(z)] dz = 1 forn = 0 0. %3D O 1,u 2n + 1 O 2,i 3 20-*

A: Introduction: The Legendre polynomial function is the solution of the differential equation…

Q: vsin ax (02+4)4= sin x is the fun ction with y %3D

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Q: 3 tari' (xty) , Prane that x2+ ydz Sen 2z be

A: We have z=tan-1x+yx-y This implies tanz=x+yx-y Let u=tanz Then we first need to find the degree of…

Q: Prove: |I| = 1. %3D

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