Find S= O S Σ3(-1) a-1 || 319 -=SO 80 O S || 43 a-1 O s-²/ 4

Q: Let = n n i=1 x₁ . Then for constants a and b, n Σ a(x₁ - ī) b² =? (6²5m)

A: The question is about parametric inference.Given :Where,X1, X2, ...., Xn are independent random…

Q: in²3xdc O 3x-sin3xcos 3x +C O 3x+sn3xcos 3x +C Bx-sn3xcos 3x 3x-sn 3rcos3x +C 3x+sn3xcs Bx +C

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Q: 5) — = [(-D)" (2-1)", when 12-1}<1. n=0

A: Introduction: A geometric series is a type of series which is in the form as follows:…

Q: Find 3 values of r n =120 o(n) such that

A: Ok

Q: 4. Write system/ 2, 3, 4. Sum the four equations to derive a simple equation for system. out in full…

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Q: To show that the general factorial function: (a)= mn (-). (+¹).(+-¹). here m is a positive integer…

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Q: 133. -Σ 2" Sn+ -(x + 2)" n=0

A: Consider the series, Rewrite this as Now take the constant outside,

Q: Evaluate: L(e* -3t * sinh 7t).

A: Given: Le-3tsinh7t

Q: (2x y 2*) (x*)(x-17) (8m'n*)(7m*n") 18a b'c 6a b

A: (a) 2x2y3z43 Simplify as, 21×3x2×3y3×3z4×3=23x6y9z12=8x6y9z12

Q: 2. (s² +5

A: The given function is -tcos5t To find the Laplace transform of the given function proceed as follows…

Q: en-3h-S If y= show that day (on-3)* 2n-3

A: Given function is  y=ex^2-3x-52x-3                           ⋯1 To show:…

Q: Find a number n e N such that 2" > 102000 and 2" has among its 2000 last digits at least 1000…

A: We will use logarithm to solve the problem

Q: If -5n-2, then f(3) is 04 O 55

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Q: (- 1)"x" Σ 6" (n² + 9) n=1 8.

A: Given

Q: Solve the following ODE y +2y +y = x + e O a. (C1+ C2) e* + (x-2) + e /9 O b. (C1 + x C2) e* + (x-2)…

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Q: 2x-3 for *く-S メ+4 %3D ーメ+3 for マ-S メ+2 for x) -5 メ+ヒ find *ビ" し 1n for order f(x) to メ- -5

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Q: dx_ -In x – 2 |x+2 X - + C x² – 4 - 4 Select one: O True O False

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Q: Show that the generating function for the number of compositions of n where each part is either 2 or…

A: To find the generating function for the number of compositions of n where each part is either 2 or…

Q: 201-25-(1-82 60 86)(So) | (o-Sh)는 (0-5h4

A: Do square both the side. Now solve 5 powered equation.

Q: dx ** Evaluate x(x + 1) 1 (A In 4 (B B In5 none of these D In 4 1 E

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Q: dx (1)(- 2e * )

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Q: Evaluate L{cos² 3t} s² – 18 a) s(s² + 36) s2 – 18 b) s(s² – 36) s² + 18 c) s(s² + 36) s2 + 18 d)…

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Q: 3 - 4 fX = the value of X" is - 1 %3D

A: We have to find the value of X^n

Q: 2x+11 1 Consider f dx = x2+x-6 x-2 x+3 then evaluate S(-dx xp(* - 3 x+3

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Q: Find residue 1 Res₂=0 24 +4% 2 Res 2 = 1 ze 3 2³-1 of

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Q: 4(-1)" Σ 3) Estimate 2N 1 correct to one decimal place. N-1

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Q: -3an The solution of the recursion relation ant1= n > 0, with ao = 1, (n+1)? " is an O None of these…

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Q: 2s (s-1)(s+2)J (s+2) Select one: O True O False

A: Let us find the inverse of RHS and LHS separately then we will compare. LHS:…

Q: 14 Let /= 8, x4 dx. Select all that apply x3 - 512

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Q: Prove: If |S| = n then |P(S)| = 2^n

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Q: Find Š Clim sup and s Clim inf) nt (-1) (znt) of Sn=

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Q: A = D −13 ๆๆ || 4 B = -2 0 1 4 3 1 -2 = 0 -4 3 -4 5 " 3|N NN M 916 | | NO

A: Given:  A=13-43-2014, B=-32725216133116, D=31-250-4-453 To Find: The value of D+AB