consider the function f(x)-In(1 - r) f(n) (0) for n 1 n! 1. Determine 2. Use your answer from #1 to determine the Maclaurin Series of f(x). Find the Radius of Convergence.

Please solve parts 1, 2, and 3 of the attached question. See BOTH attahced images.

consider the function f(x)-In(1 - r)<br>f(n) (0)<br>for n 1<br>n!<br>1. Determine<br>2. Use your answer from #1 to determine the Maclaurin Series of f(x). Find the Radius of Convergence.<br>

Extracted text: consider the function f(x)-In(1 - r) f(n) (0) for n 1 n! 1. Determine 2. Use your answer from #1 to determine the Maclaurin Series of f(x). Find the Radius of Convergence.

Note that the derivative of f(x) = -In(1-) is the function f'(a) =<br>The Macluarin Series of f'(r)<br>is known:<br>-<br>1<br>-1 <1<br>'(x)<br>0<br>Thus, another way to find the Macluarin Series of f(x) is to integrate this power series.<br>Σ<br>x term-by-term. Choose an appropriate value for your constant of<br>3. Integrate the power series<br>n=0<br>integration C such that<br>f(x)In(1) = C +<br>dar<br>1. Your answer should match the Macluarin Series found in # 2.<br>for -1<br>

Extracted text: Note that the derivative of f(x) = -In(1-) is the function f'(a) = The Macluarin Series of f'(r) is known: - 1 -1 <1 '(x)="" 0="" thus,="" another="" way="" to="" find="" the="" macluarin="" series="" of="" f(x)="" is="" to="" integrate="" this="" power="" series.="" σ="" x="" term-by-term.="" choose="" an="" appropriate="" value="" for="" your="" constant="" of="" 3.="" integrate="" the="" power="" series="" n="0" integration="" c="" such="" that="" f(x)in(1)="C" +="" dar="" 1.="" your="" answer="" should="" match="" the="" macluarin="" series="" found="" in="" #="" 2.="" for="">

Jun 05, 2022

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consider the function f(x)-In(1 - r) f(n) (0) for n 1 n! 1. Determine 2. Use your answer from #1 to determine the Maclaurin Series of f(x). Find the Radius of Convergence.

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