Question: Problem 6: (4 pts) a) Find the nth-order Taylor polynomial for the following functions centered at the given point a. f(x) = In(2 - x),

Problem 6: (4 pts) a) Find the nth-order Taylor polynomial for the following functions centered at the given point a. f(x) = In(2 - x), n= 3, a =1 b) Use your Taylor polynomial from part (a) to approximate the value of In(1.3). 1 3 Problem 7: (4 pts) Use a convergence test of your choice to determine whether the following series converge. 2k 2 k2 - 4 Problem 8: (4 pts) Use a convergence test of your choice to determine whether the following series converge. 2k K= 1 K . (k!) Problem 9: (4 pts) Does the following alternating series converge absolutely, converge conditionally, or diverge? Show work to validate your answer. (-1)*+1 3k K= 1 7k

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