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Use the formula In(1+x)= Error = r- |1n 2²/7 - n=1 (-1)^-1x n -*2²2 +²³-*+ =X- and your knowledge of alternating series to find the smallest / such that the partial sum S approximates In (Round your answers to six decimal places.) N = X SN= + for [x] <1 to within an error of at most 10-3. Confirm this using a calculator to compute both S and I d In ().

Use the formula In(1+x)= Error = r- |1n 2²/7 - n=1 (-1)^-1x n -*2²2 +²³-*+ =X- and your knowledge of alternating series to find the smallest / such that the partial sum S approximates In (Round your answers to six decimal places.) N = X SN= + for [x] <1 to within an error of at most 10-3. Confirm this using a calculator to compute both S and I d In ().

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use the formula In(1 + x) = Σ n = 1 Error = SN = In(-³) 8 to within an error of at most 10-3. Confirm this using a calculator to compute both S and In and your knowledge of alternating series to find the smallest N such that the partial sum S approximates In (Round your answers to six decimal places.) N = X | 1n / - SN| = (−1)n-1xn n = = X x3 2²+4²-X 3 + for x < 1
Transcribed Image Text:Use the formula In(1 + x) = Σ n = 1 Error = SN = In(-³) 8 to within an error of at most 10-3. Confirm this using a calculator to compute both S and In and your knowledge of alternating series to find the smallest N such that the partial sum S approximates In (Round your answers to six decimal places.) N = X | 1n / - SN| = (−1)n-1xn n = = X x3 2²+4²-X 3 + for x < 1
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