Use the power series f(x)= In (1 – x) = - for -1sx<1, to find the power series representation for the following function (centered at 0). Give the interval of com k=1 f(7x) = In (1 – 7x) Which of the following is the power series representation for f(7x)? O A. E in (1-(7x) O B. (7x)* k=1 k=1 OC. OD. 00 Tk k=1 k-1 The interval of comvergence is (Simplify your answer. Type your answer in interval notation.)

Q: Σ 1 as a rational function. Express the series x2n n=1

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Q: 3. Write the Maclaurin series of the given function, in sigma () form and write out the first three…

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Q: Find the MacLaurin series for the function f(x) = (1 + x)7. It is actually finite – it’s a…

A: Maclaurin series for f(x) is given byf(x)=f(0)+f'(0)x1!+f''(0)x22!+f'''(0)x33!+...f(x)=(1+x)7…

Q: 2. Use the geometric power series to find a Maclaurin series for the function - 4x f(x)= Use sigma…

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Q: From the following statements, choose the one(s) that are true. OA. The function f(x) = 1 can be…

A: Options A and B are incorrect because the power series representation of 11+x=∑n=0∞ (-1)nxn but the…

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

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A: soln: step1: write a fx as a power series centered at c=-1fx=22-xwe know general formula power…

Q: 4. Consider the Legendre series of f(x) = |x| over the interval (-1, 1). Do some of the Legendre…

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Q: Prove that 2e 5 2 sin (Tx/4)+1/2 dx ≤ 2e-1 1+2√2 (i) Show that zloga 7/4 dx - (log) (log x)-3/4 (ii)…

A: All the parts are solved properly with detailed explanation.Hope you got your answer. If any query…