Prove the ..... Pr |P2n-1 Pn (− 4 ) = ² ( − 12 ) Pan ( 1 ) + ¹³ ( − 1) ³²2-1 (9) + + (-))) 2 P211

Q: Given that |a| = 20, find all left cosets of (a¹2) in (a).

A: This question from topic coset of group theory.

Q: 13.Show that the third-order Adams-Moulton formula is yn+1=yn+h12(5fn+1+8fn−fn−1).

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Q: True or false: The coefficient of x4y7 in (3x – 4y)11 is (2)347. True False

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Q: 512x 1-x -3 - =—1 find volue of Σ(x²)"=? n=1

A: Given that the equation 512x1-x-3=-1   .

Q: 1 (x² - y²)² x+y valuate: ²₁₁² dx dy

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Q: (5) Solve for n EN. +2 (a) (3) = }(n+²). 5 n (b) (²) > (^).

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Q: Prove that _f₁ = = ₁+2 +851+1 −85₁-1 + ₁-2 +0(hª) 12h

A: Use taylor series expansion to prove this

Q: 20.16 Prove that (i) E (ii) (-1)"(2n + 1)-³ = 32 90 n=1

A: Note: According to our guidelines We’ll answer the first question since the exact one wasn’t…

Q: 21 _) P') pludx= чи (и+1) сеn+ л 2 и+31 и+1

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Q: 1. true or false. justify your answer. (a) Im(z) > 0, then Re(1/2) > 0. (b) Re(z12) = Re (z1) Re (2)

A: Solutions

Q: Prove or disprove: If (n) and (yn) are subsequences of each other, then n = yn.

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Q: 1. Solve for P given P' = 6t√P √² +3 with P(1) = 25.

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Q: Coider g(s) = १3 + (2x +2" Calculate g(x) : 5 3 3 A) + 6(2r - 1)* B) 3(2r-1)" C) 3V 3(2r- 1)*

A: Find your answer below

Q: 4. Prove that 3i² + i = n(n+ 1)?

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Q: 21 -2 T 5. If B= 1 -2 T = - +4 = 2 +5 1 Using two methods to find [T]B-

A: Method I- Let T be linear transformation on  a Vector space V with n dimension with basis…

Q: 35. Prove: If xn = :o(an), then xn = = O(an). Show that the converse is not true.

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Q: 3. find the Lem and hef of 12,15 andh 2kyapplying the pacene factoce. eatial mothod 2x 2x 3 3 X5 2…

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Q: Prove that TIN) F(a – p) O< Re

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Q: 2F. n 1 ;;1=2" (b), (26)

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Q: Given the formula P(X = r) = (,) p"qn=r where r=0,1,2,3,...,n and q = 1- p. %3D (a) If n=7 and…

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Q: 3. Find the sum of all values of k such that 2k k -dx =15. (A) 3 (B) 2 (C) 1 (D) 0 (E) 1/2

A: ∫12kx-kx2dx=15∫12kxdx-∫12kkx2dx=15∫12kxdx-k∫12kx-2dx=15x2212k-kx-2+1-2+112k=15x2212k-kx-1-112k=15x22…

Q: (7) Let X P(a) and E(x)= E(5-5x), then 2 is. (a) 25/26 (b) 26/25 (c) 12/26 (d) 26 (e) None of these

A: We know that the if X~P(λ), then E(X) =λ

Q: What is the coefficient of x'y5 in the expansion of (1x + 3y)18? 3,15

A: Use formula of binomial expansion to solve the question.

Q: Suppose P(Xi=1)=pi=1-P(Xi=0),  i=1,2 if p1> p2 show that X1>( greater than equal to (st)) X2

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Q: 1. Express 0.116 <р<0.192 in the form p±E

A: The given confidence interval is, The value of sample proportion is,

Q: 42. Show that S 4xys + %3D 1- x2 1- y? 1– 22 (1 – a²) (1 – 3²) (1 – 2²) if xy + xx yz = 1

A: Given that  xy+yz+xx=1 Prove that the expression

Q: For any positive integer n x¹ x* -1 = ΠΦ (x). d/n

A: Let ξ=cos2πn+i sin2πn. Then the roots of xn-1 are 1,ξ,ξ2,....,ξn-1. Thus…

Q: 1 2 1 | | (x² + y»2 + z²)dzdydx lo Jo

A: To evaluate the given triple integral: ∫-10∫02∫01(x2+y2+z2) dz dy dx=∫-10∫02∫01(x2+y2+z2) dz dy…

Q: demonstrate that

A: We have to demonstrate

Q: Prove that (0.01)(100sin2π(5000)t)2 is equal to 0.5+0.5cos2π(10000)t

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Q: 2. Prove 1+5+9+13+ .…+ (4n – 3) = n(2n – 1) using PMI. ... %3D

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Q: 4. Find ez dz fa-1+31-8 (3² + 1)(= + 9) |z-1+j|=/

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Q: B 2. 7.2.Preve that CD= 24 SnR Vzt2 cosx

A: Use trigonometric ratio to solve

Q: 5. Let h (z) = (z+1)(z+6)(z+10) z(z+2)(z+3) (z+3)(z–2)°, (z+2)(z+6) What is the residue of h (z)at z…

A: Given a function on complex plane as hz=z+1z+6z+10zz+2z+3+z+3z-22z+2z+6 Residue at z=-2 is given by…