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Expand y= sin^-1x using maclaurin's theorem...
Please give appropriate answer...
hitman86:
bro i m in class 9th so i don't know the answer
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series expansion can be used here as follows:
Series expansion at x = 0:
Sin^-1(x) =x + x^3/3! + 3^2.x^5/5! + 3^2.5^2.x^7/7! + 3^2.5^2.7^2.x^9/9! + 3^2.5^2.7^2.9^2.x^11/11!.......and so on.
This is the same as:
Sin^-1(x) = x + [1/2.3]x^3 + [1.3/2.4.5]x^5 + [1.3.5/2.4.6.7]x^7 + [1.3.5.7/2.4.6.8.9]x^9....etc.
The steps here are self-explanatory.
Series expansion at x = 0:
Sin^-1(x) =x + x^3/3! + 3^2.x^5/5! + 3^2.5^2.x^7/7! + 3^2.5^2.7^2.x^9/9! + 3^2.5^2.7^2.9^2.x^11/11!.......and so on.
This is the same as:
Sin^-1(x) = x + [1/2.3]x^3 + [1.3/2.4.5]x^5 + [1.3.5/2.4.6.7]x^7 + [1.3.5.7/2.4.6.8.9]x^9....etc.
The steps here are self-explanatory.
can you please tell me that how did you get 3^2,3^3.5^2 and so on in the expansion
*3^2.5^2
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i hope this solves your doubt
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