(a) Differentiate the series -4 1 -cos ((2k + 1)Tx) =0 (2k + 1)? term by term and plot various partial sums for that series on [0, 1]. How does this compare to the derivative of f(æ) = x - - on that interval? (b) Differentiate the series you obtained in part a and plot various partial sums of that on [0, 1]. How does this compare to the second derivative of f(x) = x - on that interval?

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A: Given: The given sequence is ann=1∞=13∫13dxx,15∫15dxx,17∫17dxx,19∫19dxx.....

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A:

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A: To Prove:z=tan1ilog1+iz1-iz12.

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A: That's easy. Have a great day!!!

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A:

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A:

Q: (-5) 1 Find the sum of the series 6T

A: The given series is an infinite geometric series and its sum is S=a/1-r,r&lt;1.  See 2nd step.

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A:

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A: Given series is

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A:

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A: Step 1:Step 2:

Q: What is the second term in the power series expansion of f(x) = e^x?

A:

Q: (b) If f(x) = E anx", specify the domain of f. n=1 Based on your answer in Question 2(b), explain…

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A: we have to find the coefficient of x^5

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Q: The formula provided in the question is a power series representation for g(x)= e-x^2

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A:

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A: Formulae: 1. e-x = 1-x/1! +x2/2! - x3/3! +x4/4!- ....... 2. d/dx{ e-x} = - e-x   Answer: f'(x)= f(x)