Which one of the following correctly finds the Taylor Series and the Interval of Convergence about the centre c = 1 for the function f(x) = ln(3x − 2)? O Taylor Series does not exist Σ Taylor Series Σn=0 (-1) (3(x-1))+1 n+1 Taylor Series does not exist Taylor Series n=0 (-1)³ (3(x-1))+1 n+1 Interval of Convergence does not exist Interval of Convergence 3 Interval of Convergence -∞0≤x≤00 Interval of Convergence -∞0≤x≤00

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Q: 6.) E (22-1)(2k +1) k-1 (21

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A: The given Taylor series centered at 0 for arctanx is ∑n=0∞-1n2n+1x2n+1. We have to find the Taylor…

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A: The function, fx=ex2.

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A: Consider the equation as shown below: Here, function fxcentered at x=2 is given by ∑n=0∞3nn+1!x-2n…

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A: using ratio test to find interval of convergence.

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Q: (x+ 2)" n . Find the interval of convergence of the power series n3" n=0 (A) [–1,5) (B) [–1,5] (C)…

A: Solution:- ∑n=0∞x+2nn 3n un=x+2nn 3nun+1=x+2n+1n+1 3n+1 limn→∞ unun+1=limn→∞ x+2nn3nn1+1n3n+1x+2n+1

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A: Taylor series solution

Q: 11) Test the series for con convergence E (-1)^ sin² (3n) n n=1 = Compute the derivative d br an…

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Q: Given the function ƒ(x) : Which one of the following f? -∞0 < x < ∞ 5 5 0-11 <²0 11 ○ (-끝,끝) - (-1,…

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Q: Find the Taylor series centered at c = -1. %3D f(x) = e5x %3D

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Q: 00 1 1 Given that with center x" with convergence in (-1, 1), find the power series for 1+ 6x5 1- x…

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Q: Let f(x) = X" and g(x) = x3 f (x2/25). Let anxn be the Taylor series of g about 0. The radius of…

A: Given function is fx = ∑n=1∞ xnn  and  gx =x3  f x225 Note:- x225 =x52