(3) (a) Determine whether the series is convergent or divergent. Explain why. n (b) Show that the function f(z) = zsin- has no limit as the complex variable z → 0. Z (Hint: Try to approach 0 along two different paths.)

Q: Determine the sequence of the generating function A(s) = (1– 2 -9)2 |s| < 1

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Q: 04: A) Consider the sequence (f,(x) of functions f,:R→R defined by: f.x)=Cos"(x) for-a/25xSa/2.…

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Q: 5. Consider the equation f(x) = x - 2- = 0. (a) Show that the above equation has a solution on the…

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Q: Theorem 17 (H.w) If lim x, # 0 then E=1Xn diverges series.

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Q: Theorem 1.5. Consider the absolutely convergent series S(x) = ao + a1x + a2x2 + ...+ akx* + ·..,…

A: Given: The given series is Sx=a0+a1x+a2x2+.....+akxk+...

Q: ((-1)" Determine (with justification) whether the series is absolutely convergent, conditionally n°…

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Q: 2. The Taylor series for a function f about x 1 is given by (-1)*1 (x-1)" and converges to f(x) for…

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Q: (i) Let F(x) be a power series. Then the radius of convergence of F(x) can be negative.

A: This is a problem related to power series. Please follow the procedure given below.

Q: Analyse the convergence of the sequence {fn} where fu(x) = on R. 1+ na²

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Q: Expand g(z) = (1-z) (2+z) as a series in the annulus 1 < |z| < 2.

A: Given ,             as a series in the annulus

Q: If 2 Cnx" is convergent when x=2 and divergent when x=-3, then 2 Cn is n=0 n =0 convergent. O…

A: Consider the given information: The series ∑n=0∞Cnxn is convergent when x=2 and divergent when x=-3.…

Q: 3. Determine the convergence or divergence of the following series (a) E ()" ( b) Σ ( ) (e) Σ n3D1…

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Q: If series , an converges, then limn- an – an-1) = 0 m=D1

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Q: 9) n+3"

A: Comparison test for series of positive terms states that, If an, bn are two series such that…

Q: a) Use the divergence test to determine whether converges or not. (-1)**'n n(3n² +1) b) Use…

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