The Maclaurin series for sin−1(x) is given by sin−1(x) = x + [infinity] n = 1 1 · 3 · 5 (2n − 1) 2 · 4 · 6 (2n) x2n+1 2n + 1 . U se the first five terms of the Maclaurin series above to approximate sin−1 3 7 . (Round your answer to eight decimal places.)
1 answer:
Answer:
0.44290869
Step-by-step explanation:
The Maclaurin series for sin⁻¹(x) is given by
sin⁻¹(x) = x +
Use the first five terms of the Maclaurin series above to approximate sin⁻¹ . (Round your answer to eight decimal places.)
Answer
sin⁻¹(x) = x +
in the above equation summation from n=1 to ∞
we are estimating this for the first 5 terms as follows
sin⁻¹(x) = x + + + +
sin⁻¹(x) = x + + + +
now to get
sin⁻¹( ) substitute
hence,
sin⁻¹( ) =
sin⁻¹( ) = 0.42857142 + 0.01311953 + 0.00108437 + 0.00011855 + 0.00001482
= 0.44290869
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