Prove that -i, i are the unique branch-points of arctan. In other words, show chat there does not exist a series centered at +1 that serves as a local inverse of san. Conversely, show that such a series exists for all zo ¢ {-i, i}.

Q: ind positive constants b and n, such that 3n + 2 n.

A: Finding the values of b and no

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A:

Q: [In (a* + 3) – In (2r* –- 1)] In (2r³ – 1) 7. lim

A: Definition used -             Limit of a rational function -             If limit x tends…

Q: 3. 2+z-z² EX 5: Find the Laurent series of f(z)= Sol: (2)- a 17121 (

A: Laurent series expansion

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A:

Q: 10. Let f be a continuous function with period 27. If f is an even function (that is, ƒ(x) = f(−x)…

A: The function  is continuous  with period and  is even that is Given  Claim:  for every .

Q: Q6 A periodic function is defined as: - nst< 0) F(1) = {"_2 0st<n a) Sketch the graph of the…

A: Solution

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A: Given that gt=t2    0&lt;t&lt;20t=0

Q: C. f(k)= sen4k = 0 si si 0<k< π<k< 2π

A:

Q: ‚ = (-1)" (1 - -/-/-) II) b = cos((2n + 1)π) 18.Which of the sequences converge: I) an a) I only b)…

A: (.) Given sequences are ,             and      (.) A sequence is convergent if the limit of the…

Q: Consider the following. (A computer algebra system is recommended.) -20- . -3 sxs0, x + 6) - ) Ox<…

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Q: (q) {0,1,2, 4, 8, 16} (s) s) {÷ :n E N and n is prime} (u) {x² : x € R} (w) {sin(): n E N} n 3

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Q: Oppgave 2 a) En periodisk funksjon er definert som (2x + 2 -3≤x≤0 f(x) 0<x<3 = -2x + 2 f(x) = f(x+6)…

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Q: Let f(8) = 202, 0<0 < 5 ; f(8) = f(8 + 5). %3D a) Find the Fourier coefficients; and b) hence…

A: Given function is           f(θ)=2θ2, 0&lt;θ&lt;52l=5,   l=52 Also…