The Taylor expansion of f (z) = ze2+1 around z = -i is %3D (--1)! equal to the above O None of these -iel-i + E e-( + )" (n-1)! (n-1)!

Q: 12) Let y(x) = Enzoan be a solution of y" - 2xy' - 2y = 0. recurrence relation is given by (n+2)an+2…

A: Given recurrence relation for the given differential equation is

Q: Evaluate z' if z = [1 + (x² − 1)³] ²³ O a. 2(2²-1)² (1+(2²_1)²³) i O b. none of these О с 41(2²-1)²…

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Q: Let yk = k", where n is a positive integer; then Ak" = (k + 1)" – k" - (1.112) nk"-+ n kn-2 +...+ 2.…

A: We have to solve given problem:

Q: a. Σχy, i=1 b. Σ(x)(y) C. (Σ' (Σ'

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

Q: Show m*[(1+alpha/m)^m-1] is monotonic decreasing.

A: To show that the expression m*[(1+alpha/m)^m-1] is monotonic decreasing, we need to show that its…

Q: Show that z / [(z-1)(z-3)] = -3 Σ [(z-1)n / 2n+2] - [1 / (2(z-1))] for 0 < |z - 1| < 2.

A: by using techniques of partial fractions and series expansion of 1/(1-x)

Q: Let f(z) Then the Laurent expansion of f (z) around z = 0 with |z| > 3 is: z(z-3) a ) Σ . 3n b) E…

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Q: please help with textbook question.

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Q: Compute fx²³ In (8x) dx a) = 6 x + [+\n (8x)=1] + C 4 b)x+ [4\n(8x) +1] +C c) = x²4 [4Ln (8x) + 1] +…

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Q: The generating function of a_{n+1}=8a_{n}+4n*, where a,=3 is a. Σ2x)^k+Σ (4x) ^{k Ο b. Σ( 2x) ^{k}+…

A: To find the generating function of an+1=8an+4n+1 First multiplying the relation by xn and taking…

Q: 25. Which is the correct expansion of (x + 4y)³ using the binomial theorem? O ○ (x + 4y)³ = (3)…

A: Given, (x+4y)3

Q: (11) 11. Prove by induction that 1 1 1+ + + 22 3² + - 2.

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Q: show that 11 1+ 1 n-1 1 n(ā-μο)2 Σ=1(xi-x)2 n/2 n(ā – μο)2 Σ=1(α; - z)2 (xi

A: We need to prove that:

Q: n² – 1 E(A) Given that Var(R;) = Var(R,) : 12 12n n +1 + 12 E(A) and Cov(R¡, R¡) 12n(n – 1) for i #…

A: By definition, CovaX,bY=abCovX,YCovX+a,Y+b=CovX,Y

Q: Which transformation has been performed first in the series ABCD → A'B'C'D' → A"B"C"D" shown below?…

A: topic -transformation

Q: The generating function of a_{n+1}=8a_{n}+4*, where a,=3 is Ο a. Σ2x)^+Σ (4x) ^Κ O b.…

A: Given an+1=8an+4n+1 Multiply the recurrence relation by xn an+1xn=8anxn+4n+1xn…

Q: Equate the coefficients of the quadratic term in the Taylor expansion of cos x to the corresponding…

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Q: Please can you solve it fast 18) What are the 4-point Discrete Fourier Transform (DFT) coefficients…

A: The sequence of xn is given by , xn=δn+δn-2+δn-3 The 4 point of DFT of xn , Given that N=4 ,…

Q: The 4th term in the expansion of (2x -3x 10 is 10 C4 (2a) (-3x)³ O 10 C4 (2a2) (-32)4 10 C (2)…

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Q: 21) f(x)=47x A) (4 ln 7)47x Write summation notation for B) (7ln 4)47x x(In 2) C) (In 4) 47x x(In x)…

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Q: 2)What are the first four terms of the Taylor series for ex when a = 1? e= = e+e(x – 1) + že(x – 1)?…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 16. Find the term containing x18 in the binomial expansion of (x2- y)15.

A: A binomial expression is an expression of the form a+bn. This binomial expression can be expanded…

Q: 11. Which is the correct expansion of (x + 4y) using the binomial theorem? O(x+4y)³ = (x) (4y) +…

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Q: 36. Use the binomial theorem to expand (2x - y)* . A. 16x* – 32x³y + 24x²y² – 8xy³ + y* С. 2x - 4х3у…

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Q: H(n) = 2H(n − 1) + 1, n ≥ 2, H(1) = 1 ⇒ H(n) = 2" – 1↓ Using mathematical induction, verify that our…

A: We prove result in following way. Base Case: Result is true for n=2. Hypothesis : Assume result is…

Q: 4) (n* + 12n² + 37n² + 21n – 27) ÷ (n+ 3) |

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Q: Determine the coefficient of the x'y term in the expansion of (2a + 3y) 2.

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Q: The Taylor expansion of f for x→ 10 is f(x) = 10 + 3(x-10)² + 2(x-10)³ + 0((x a) ft (10) = -12 6) fr…

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Q: RECURSION RELATIONS: L Jp(x}] = ° Jp=1(x), d.r Jp-1(x) + Jp+1(x) =2J,(x). Jp-1(x) – Jp+1(1) =…

A: As per our company guidelines, we are supposed to solve only the first three subparts. Kindly re…

Q: Find the coefficient of x' in the expansion of: (а) (1 — г) -4г3 (c) x (1+ x* (b) (1 — г)-2т8 (d)…

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Q: 5. Use the binomial theorem to prove that C(n, 0) C(n, 1) + C(n, 2) + (-1)"C(n,n) = 0. —

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Q: 4z +5 a) Solve the all possible Laurent's expansions of the function f (z)=; about the (z-1)(z-3)…

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Q: State De-Moivre's theorem. Compute n" derivative of the function y th x² +a?

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the disjunctive normal forms of the following Boolean expressions (showing all the working)…

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Q: 7 Find the coefficient of x in the expansion of ( 3x2 3x A. -105 В. 567 С. 1701 D. 504 Е. 386 F.…

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Q: The Taylor expansion of f (z) = ze²+2 around z = -i is O None of these E-e2-i (z + i)" (n-1)! equal…

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