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Recall the power series expansion for = E=o(-1)"x"= 1-x+x² - x³ + ...on the interval(-1, 1). 1+x i. Use the given expansion to derive a power series expansion for 1 1+x2 Show at least 4 non-zero terms. ii. iii. Use the expansion in part (i) to find a power series expansion for tan¹(t) = f₁2dx. 1+x² Show at least 4 non-zero terms. Use the expansion in part (ii) to approximate tan-¹ (0.1) to within 0.000001. Round your answer to 6 decimal places.

Recall the power series expansion for = E=o(-1)"x"= 1-x+x² - x³ + ...on the interval(-1, 1). 1+x i. Use the given expansion to derive a power series expansion for 1 1+x2 Show at least 4 non-zero terms. ii. iii. Use the expansion in part (i) to find a power series expansion for tan¹(t) = f₁2dx. 1+x² Show at least 4 non-zero terms. Use the expansion in part (ii) to approximate tan-¹ (0.1) to within 0.000001. Round your answer to 6 decimal places.

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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18. Recall the power series expansion for interval(-1, 1). i. ii. iii. 1 1+x - - Σo(-1)"x"= 1-x+x²-x³ +...on the Use the given expansion to derive a power series expansion for Show at least 4 non-zero terms. 1 1+x2 Use the expansion in part (i) to find a power series expansion for tan¹(t) = So 1+x²² dx. Show at least 4 non-zero terms. Use the expansion in part (ii) to approximate tan¹(0.1) to within 0.000001. Round your answer to 6 decimal places.
Transcribed Image Text:18. Recall the power series expansion for interval(-1, 1). i. ii. iii. 1 1+x - - Σo(-1)"x"= 1-x+x²-x³ +...on the Use the given expansion to derive a power series expansion for Show at least 4 non-zero terms. 1 1+x2 Use the expansion in part (i) to find a power series expansion for tan¹(t) = So 1+x²² dx. Show at least 4 non-zero terms. Use the expansion in part (ii) to approximate tan¹(0.1) to within 0.000001. Round your answer to 6 decimal places.
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