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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?
 one year ago
 one year 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?
 one year ago
 one year ago

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

AustralopithecusBest 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 \[\sum_{n=0}^{\infty} \frac{(1)^{n}(\pi x)^{2n+1}}{(2n+1)!}\]
 one year ago

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

91Best 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
 one year ago

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

91Best 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!
 one year ago
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