practfinal Sol - 1 Problem 1(10 pts 1(a(3 pts Express as a...

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1Problem 1(10 pts)(a)(3 pts) Express11-xas a geometric series and write it using the summation notation.What is the interval of convergence of this geometric series?(b)(4 pts) Using the result of Part (a), find the Maclaurin series for12ln1+x1-x, and write itusing the summation notation.(c)(3 pts) Calculate the approximate value ofln119by evaluating the polynomial using onlythe first 2 nonzero terms of the Maclaurin series obtained in Part (b) at an appropriatex.
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3Problem 2(10 pts)Consider the functionf(x)=lnx.(a)(5 pts) Approximatef(x)by a Taylor polynomial of degree 2 centered atx=2.(b)(5 pts) How accurate is this approximation when1x3?
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