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

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

DoubleCook
 2 years ago
Best ResponseYou've already chosen the best response.0Mmm 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? :/

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

timo86m
 2 years ago
Best ResponseYou've already chosen the best response.0I am sorry i suck at sigma notation

DoubleCook
 2 years ago
Best ResponseYou've already chosen the best response.0Oh haha don't worry about it, thanks anyways! :]

EulerGroupie
 2 years ago
Best ResponseYou've already chosen the best response.1I think the 1/2 and the minus are outside the sigma.

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

DoubleCook
 2 years ago
Best ResponseYou've already chosen the best response.0Oh outside? Great, thanks a lot! :]
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