Carry out the details in the introductory example to this chapter by first deriving the Taylor series for ln(1 + x) and computing ln 2 ≈ 0.63452 using the first eight terms. Then establish the series ln[(1 + x)/(1 − x)] and calculate ln 2 ≈ 0.69313 using the terms shown. Determine the absolute error and relative errors for each of these answers.
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