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Australopithecus
 3 years ago
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?
Australopithecus
 3 years ago
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?

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

Australopithecus
 3 years ago
Best ResponseYou've already chosen the best response.0I 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 \[\sum_{n=0}^{\infty} \frac{(1)^{n}(\pi x)^{2n+1}}{(2n+1)!}\]

91
 3 years ago
Best ResponseYou've already chosen the best response.1so let's start taking derivative

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

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

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