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Maclaurin-Taylor Series

 
 
Reply Wed 7 May, 2008 06:39 pm
what is the Taylor series of arcsin x ?
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Vengoropatubus
 
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Reply Wed 7 May, 2008 09:13 pm
This sounds suspiciously like homework, in which case I will remind you that the answer to your question depends on where you center the series, since arcsin x isn't a continuous function.
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mars90000000
 
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Reply Thu 8 May, 2008 12:09 pm
dont worry, its not a homework problem, our homeworks are with the sine, cosine, tangent, natural logarithms and e^something. arcsine isnt one of them, unfortunatly, try centering arcsine around 1 ; since arcsine of 1 is equal to pi over 2, i just wanted to know the taylor serie of arcsine to then replace x by 1 and have the value of pi in an infinite sum...

oh an another question, for the taylor series of sinh x can we do the taylor series of (e^x - e^-x)/2., same for cosh using (e^x + e^-x)/2 and tanh using sinh/cosh? im pretty sure we can but just making sure. so yea, try the taylor series of arcsin x centered over 1...
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High Seas
 
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Reply Thu 8 May, 2008 01:16 pm
Re: Maclaurin-Taylor Series
mars90000000 wrote:
what is the Taylor series of arcsin x ?


You probably want the Chebychev and not the Taylor expansion. More, here:

http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/arcsin/fastsqrt.html
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