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What is the series expansion of sin^-1(x) at x = 0. Please give 3-5 terms of the expansion with steps if possible.Thanks for your help.

 Jun 12, 2017
 #1
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Taylor Series  around x = 0

 

x + x^3/6 + (3 x^5)/40 + (5 x^7)/112 + (35 x^9)/1152 + (63 x^11)/2816 

 

 

cool cool cool

 Jun 12, 2017
 #2
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Taylor 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.

 Jun 12, 2017

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