7-1 let f(z) = (z²+z) e²-1, and C: 121-3 be a circle in Positive Sense. Then. i-write the laurent series for f in 02-1/²00 - Find the redu residue of f ii- Use the residue to Evaluate (fcz) dz

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Q: Express the number ln(1.2) as a sum of an infinite series.

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Q: 9. (a) Find the first four terms of the Taylor Series for f(x)= e with a = 0. Start from the very…

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Q: (3) Give an example of a series 1 Cn that diverges even though cn < 0.0000001 for all n and limn→∞…

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Q: Bsinh lan da bs dx C√x 0 using the first four terms of the series if a = 2, b = 10, c = 6, k = 0.63,…

A: We know  sinhx=x+x33!+x55!+x77!+... ∫0kbsinhaxncxdx=∫0kbaxn+axn33!+axn55!+axn77!cxdx…

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Q: gence of a sequence, prove that the following statements are true. (a) lim 2n+1 5n+4 nx (b) lim 2²…

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Q: Find the four terms of a power series in x for the given function. (а) есos х (b) cosh x In (1+x)

A: a) Given function, e-xcosx Since, the power series of e-x and cosx is given by,…

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A: fx=14-x

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Q: Ο 16 Σo (-4)*2 (-1)"2n 4"+2 το 2n=0. που Σ 16 =0 (-1)" ²n 4+2 Σo (4)"an 16 Σño (4)"a2 mari Find a…

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Q: k-1 Since the series can be rewritten in the form >4 (G) it is a geometric series with: k=1 a = Give…

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Q: The Maclaurin series for a function is given by (-3)^-¹ (-3) -1 71 converges to f(x) for x < R,…

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