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DoubleCook
Group Title
What is the Taylor series for f(x)=sin^2(5x)?
Hint: using the identity sin^2 x = 1/2 (1cos(2x))
 one year ago
 one year ago
DoubleCook Group Title
What is the Taylor series for f(x)=sin^2(5x)? Hint: using the identity sin^2 x = 1/2 (1cos(2x))
 one year ago
 one year ago

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timo86m Group TitleBest ResponseYou've already chosen the best response.0
\[( \left( \sin \left( 5\,a \right) \right) ^{2}+10\,\sin \left( 5\,a \right) \cos \left( 5\,a \right) \left( xa \right) + \left( 25\, \left( \sin \left( 5\,a \right) \right) ^{2}+25\, \left( \cos \left( 5\,a \right) \right) ^{2} \right) \left( xa \right) ^{2}{ \frac {500}{3}}\,\sin \left( 5\,a \right) \cos \left( 5\,a \right) \left( xa \right) ^{3}+ \left( {\frac {625}{3}}\, \left( \sin \left( 5\,a \right) \right) ^{2}{\frac {625}{3}}\, \left( \cos \left( 5\,a \right) \right) ^{2} \right) \left( xa \right) ^{4}+{ \frac {2500}{3}}\,\sin \left( 5\,a \right) \cos \left( 5\,a \right) \left( xa \right) ^{5}+O \left( \left( xa \right) ^{6} \right) ) \]
 one year ago

timo86m Group TitleBest ResponseYou've already chosen the best response.0
Something like that?
 one year ago

DoubleCook Group TitleBest ResponseYou've already chosen the best response.0
Mmm what is it using the sigma notation? I was thinking something like \[\sum_{0}^{\infty} (1/2) \frac{ 1/2 (1)^k (10x)^{2k} }{ (2k)! }\] but my homework says it's wrong? :/
 one year ago

DoubleCook Group TitleBest ResponseYou've already chosen the best response.0
http://www.webassign.net/userimages/knownseries.jpg?db=v4net&id=154152 I used this
 one year ago

timo86m Group TitleBest ResponseYou've already chosen the best response.0
I am sorry i suck at sigma notation
 one year ago

DoubleCook Group TitleBest ResponseYou've already chosen the best response.0
Oh haha don't worry about it, thanks anyways! :]
 one year ago

EulerGroupie Group TitleBest ResponseYou've already chosen the best response.1
I think the 1/2 and the minus are outside the sigma.
 one year ago

EulerGroupie Group TitleBest ResponseYou've already chosen the best response.1
\[\frac{1}{2}\frac{1}{2}\sum_{0}^{\infty}\frac{(1)^{k}(10x)^{2k}}{(2k)!}\]
 one year ago

DoubleCook Group TitleBest ResponseYou've already chosen the best response.0
Oh outside? Great, thanks a lot! :]
 one year ago
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