Let b>0. Is the series of function below uniformly convergent on (b,b+1) ? Give complete proof. > [(x – b) · In(x – b)]" n=1

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A: from geometric series,

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A: We find a power series representation and radius of convergence of  f(x)=x/(1+4x)2 .

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A: According to bartleby guidelines we can only solve one question at a time. So kindly upload another…

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A: Given - fx = 5x + 18x2 + 9x + 20 about x = 2 To find - Find a power series representation for the…

Q: er divergen HiW.Which of the fallowingseries converge Ln n

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Q: а. f(x) = 1– 4x? 4 b. f(x) = 2х + 3 X С. f(x) .2 2х + 1 (2х — 1)" |

A: According to the guidelines, the first 3 questions will be answered.

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A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the next…

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A: Given that, g(x)=4xx2+2x-3g(x)=4xx2+3x-x-3g(x)=4xxx+3-1x+3g(x)=4xx+3x-1

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Q: Find a power series representation for the function and determine the interval of convergence. 3 f…

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A: It is known that the Maclaurin series is given by, Replace x by –x2 as follows.

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A: First we write expansion of tan-1x and then replace x by x3. And again multiply it by x2. Then find…

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Q: Prove that the Maclaurin series for the function f(x) = sinh x converges to the function for all x.

A: The given function is fx=sinh x. It is same as sinh x=ex-e-x2.

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A: SOLUTION-

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Q: Find a power series representation for the function and determine the radius of convergence: f (x) =…

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A: The solution is given in the next step.

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Q: c) Use the Integral Test to determine whether the series divergent. Show your work. is convergent or…

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