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Australopithecus
Group Title
Use the Maclaurin Series for f(x) using the definition of the Maclaurin Series for
sin(pix)
Can anyone show me how to find the series using the Maclaurin method?
 2 years ago
 2 years ago
Australopithecus Group Title
Use the Maclaurin Series for f(x) using the definition of the Maclaurin Series for sin(pix) Can anyone show me how to find the series using the Maclaurin method?
 2 years ago
 2 years ago

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91 Group TitleBest ResponseYou've already chosen the best response.1
f(0) f'(0)(x0) f''(0)(x0)^2  +  +  0! 1! 2!
 2 years ago

Australopithecus Group TitleBest ResponseYou've already chosen the best response.0
I just memorized the table the answer is, but it would be nice to know the method to this as it will probably come up on my final \[\sum_{n=0}^{\infty} \frac{(1)^{n}(\pi x)^{2n+1}}{(2n+1)!}\]
 2 years ago

91 Group TitleBest ResponseYou've already chosen the best response.1
so let's start taking derivative
 2 years ago

91 Group TitleBest ResponseYou've already chosen the best response.1
f'(0)= pi cos(pi x) = pi f''(0)=pi^2 sin(pi x)=0 f'''(0)=pi^3 cos(pi x)=pi^3
 2 years ago

91 Group TitleBest ResponseYou've already chosen the best response.1
so you see the pattern pi, 0, pi^3,0,pi^5,0,pi^7
 2 years ago

Australopithecus Group TitleBest ResponseYou've already chosen the best response.0
right
 2 years ago

91 Group TitleBest ResponseYou've already chosen the best response.1
so you can put it into the series format pi x  pi^3 (x)^3 + pi^5 (x)^5    ..... 3! 5!
 2 years ago
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