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4 A certain computer algorithm used to solve very complicated differential equations uses an iterative...

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Calculus

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4 A certain computer algorithm used to solve very complicated differential equations uses an iterative method That is the algorithm solves the problem the first time very approximately and then uses that first solution to help it solve the problem a second time just a little bit better and then uses that second solution to help it solve the problem a third time just a little bit better and so on Unfortunately each iteration each new problem solved by using the previous solution takes a progressively longer amount of time In fact the amount of time it takes to process the k th iteration is given by T k 1 2k 1 seconds I A Use a definite integral to approximate the time in hours it will take the computer algorithm to run through 60 iterations Note that T k is the amount of time it takes to process just the k th iteration Explain your reasoning B The maximum error in the computer s solution after k iterations is given by Error 26

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