the convolution theorem) e" dr re" (b) С (d) L{ / rsin(r) dr re" dr

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

A: De Moivre's theorem states that: cosθ+isinθn=cosnθ+isinnθ for all integers n. Also, it extends to:…

Q: 1-n let u = y – derive both sides %3D L.rit x 1--1 Chain rule .

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Q: Existence and Uniqueness Theorem ap (h) u(1) (o) aul 1)

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Q: Theorem-e Gaey-Hemiltion)let Aexz motrix

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Q: -4z2-4 Let C: |z-1=3 and I = dz. Then z2-1 I=-2nti |=0 (without applying Cauchy-Goursat Theorem)…

A: we use the Cauchy residue theorem to evaluate this...

Q: Proof IP A SD and Dis olosed. Then A' D

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Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

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Q: 1- iz If z = x +i y and w = z-i show that |w| = 1-z is purely real

A: i2 = -1

Q: 21. Write a proof of the Side-Side-Side Similarity 67° 20 A0 RER Theorem. elpr AB BC EF _ AC Given:…

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Q: 6. Given: VT bisects ZSTU. LU LS Prove: ASTV AUTV T. Proof: Statement Reason 1. 1. 2. 2.

A: Given: VT bisects ∠STU, ∠U=∠S. Since VT bisects ∠STU, therefore, ∠STV=∠UTV

Q: DHinew the porition nertor ae a fun ction of tne Find v(t) and a (t)

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Q: 1). Let, 2=x+iy *,y€R. In this case, (a). Prove the equations 2-2+2 and a = i.2 %3D %3D

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Q: State Cayley-Hamilton theorem. Verify Cayley-Hamilton theorem [1 LA 13 1 -1 -1 1

A: Cayley–Hamilton theorem: This theorem states that every square matrix satisfies its own…

Q: 4z2+4 Let C: |z+1|=4 and I = dz. Then z²-1 O None of these O I=-2ni O l=0 by Cauchy-Goursat Theorem…

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Q: 4. Using Z(n)= Show that Z(ncos no) = (z-1) (z'+2)cos0-2z (2-2zcos0+1)

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Q: If B,>3, then a measure of kurtosis is Leptokurtic Mesokurtic Platykurtic None of the above

A: In question, We'll discuss about measure of kurtosis.

Q: Using OLS or any other suitable method, Prove that E(B1) = B1 %3D E(Bo) = Bo %3D

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Q: QuestibaNo1e 4k R 18 an unit element, then. întegral doman with every unit n R is a unit in Rf9 and.…

A: Just use definition of unit and result will follow.

Q: (응) cost/ of the funcfion 4) EStimate the vawe of In osing a linearization f(e)> In (x) cos² (x).

A: Given: The function fx=lnx cos2πx To estimate: The value of ln65cos26π5 using linear factorization.

Q: 1. (8 points) Let x, y ER" be given. ||||||y||= (a) If 1 and 2 y = 1, show that a = y. (b) If | ≤ 1…

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Q: 1. Find a formula for A" using the diagonalization process (A" = PD' p'). Show all the work.

A: We need to diagonalize the matrix.

Q: b) Given that z, = V3 +i and z, = -2- 3i . Find the modulus and argument of and %3D Hence, express…

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Q: 5. What information would you need to conclude that ANLT 2 DIE using the SAS Congruence Theorem?…

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Q: Theorem 2. Let a, b, c E Z such that gcd(a, c) = gcd(b, c) = 1. Then gcd(ab, c) = 1. %3| Proof.…

A: the gcd of two integers is the largest positive integer that divides each of the integers.

Q: -4z2-4 Let C: z-1|=3 and I = 4, dz. Then z2-1 O None of these O I-0 (without applying Cauchy-Goursat…

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Q: -3z²-3 Let C: |z – i| = 4 and I = . dz. Then z2-1 1=-2ti None of these O 1-2rti O 1=0 (without…

A: Given that: C:|z-i|=4 and I = ∮c-3z2-3z2-1dz

Q: rk HIJK is a ki

A: It is given that ,  Quadrilateral HIJK is a Kite ,

Q: -4z2-4 Let C: |z-1=3 and I = $. =*dz. Then z²-1 |=0 (without applying Cauchy- Goursat Theorem) O…

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Q: 6) State Euler's Theorem. a Show thet the Cobb- Douglas Productior Function Q(K, L) = AKa L with a +…

A: Euler's theorem for homogeneous function is stated as If fx,y is a homogeneous function of degree n,…

Q: -4z2-4 Let C: z-1=3 and I = dz. Then z2-1 O I=-2ni O l=2ri I=0 by Cauchy-Goursat Theorem |=4rti I=0…

A: According to our guidelines we can answer only first question. We use Cauchy Residue theorem to…

Q: -4z2-4 Let C: |z-1|=3 and I = $. dz. Then z2–1 |=-2nti |=0 (without applying Cauchy-Goursat Theorem)…

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Q: Q) let P aprobabiity funckion on S: La,a,a) Find plai) If:- i) pcaz) = and plas) = ii) pc{ãa, az} ,…

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Q: atation for f(r) = In(5- a) and %3D

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Q: Let z E (-1,0) and let R. (z) be the remainder in Maclaurin's formula for In(1+2) in Cauchy's form.…

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Q: Using Euler's equation, show that-: zSinø z{(KØ)} = z2 – 2zCosØ +1

A: The solution is given below

Q: Proof #1) A Given AC = CB Dis the midpoint of AB Prove: AACD ABCD

A: It is given that, AC=CBD is the midpoint of ABWe have to prove that, △ACD≅△BCD.

Q: 6. A cable for a su sp en si on bridge has the sh ape of a parabol a with eqation y = kx². Let h…

A: Solve the above problem.

Q: -4z2-4 Let C: |z-1|=3 and I = Pc 7?-1 dz. Then O I=2ni O I=4rti |=0 (without applying Cauchy-…

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Q: nozmal subgsoup H of ozder 4 of subquoup H of order 4 of Consieles dihedral poove that a Dy= Lasbi…

A: It is known that; Next, we show;

Q: given a//b//c  and Bis the mid point of AC.  AB= 2x+3 BC= x+7 DE= 3x+2 Find EF.

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Q: -3z2-3 Let C: |z – i| = 4 and I = f. dz. Then %3| z2-1 I=2ri |=0 by Cauchy-Goursat Theorem |=0…

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Q: roblem 1. Show that if (x, y, z) is a Pythagorean triple then 60|xyz.

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Q: 2] a) If A. B = AB cos(0), then show that |A. B| < |A|. |B|.(Cauch-Schwarz inequality).

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Q: ...+(2n-1) = na prove that 1+ 3+5+ n= 1,2,3.. pin)=D1+3+5 tere +(2n-1) = n² %3D %3D

A: Given 1+3+5+··············2n-1=n2     .............1 Where n=1,2,3,...... Use the formula for the…

Q: K=(0,20) ) Show (K,0,0) field. 12) Show (2,t,)(K,Ð ¸º) Hlint: : fi R ->K, fa)=e*]

A: As per our guidelines I am only solving 1st. For 2nd kindly resubmit the question mentioning 2nd.

Q: ABC is an isosceles triangle Where AC=√√3 AB O is an origin such that TÀI LI DB-Z₂ De-Za Suppose arg…

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Q: Ouestion 01 f JeRla.b] and if hicx)-912) for finite mumber of Point except in [asb] then b. and…

A: Set ε&gt; 0. Since g ∈ R[a,b],  there exists a partition P = {a=x0,x1,...,xn−1,xn = b} such thatU(P,…

Q: (NAS 4) Given, A = x²zî – 2y°z²j + æy?zk Find divAat the point (1, –1, 1)

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Q: 5. Proving (Learning Packet #2) Given: 2CXA LABX AX bisects LBAC Prove: ACXA ABXA Reason Statement

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