Solved: A square root finder A well-known method for
Chapter 8, Problem 82(choose chapter or problem)
A square root finder A well-known method for approximating 1c for a positive real number c consists of the following recurrence relation (based on Newtons method; see Section 4.8). Let a0 = c and an + 1 = 1 2 aan + c an b, for n = 0, 1, 2, 3, c. a. Use this recurrence relation to approximate 110. How many terms of the sequence are needed to approximate 110 with an error less than 0.01? How many terms of the sequence are needed to approximate 110 with an error less than 0.0001? (To compute the error, assume a calculator gives the exact value.) b. Use this recurrence relation to approximate 1c, for c = 2, 3, c, 10. Make a table showing the number of terms of the sequence needed to approximate 1c with an error
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