Posted by **KIKSY** on Tuesday, March 8, 2011 at 9:33pm.

Thankyou very much!

I'm having trouble with this question about taylor series.

how would i go about doing the following questoin?

thank you!

find the maclaurin series for the function

sin(x)-x+((x^3)/3!)

how do i do this?

thanks aagain

- Math -
**MathMate**, Tuesday, March 8, 2011 at 11:43pm
A Maclaurin series expansion is a power series expansion about 0.

Thus:

f(x)=f(0)+f'(0)*x + f"(0)*x^2/2! + f^{(3)}(0)x^3/3! + ....

for sin(x),

all the even ordered derivatives (f(0),f"(0)...) are sin(0), so the terms left are:

sin(x)=cos(0)x-cos(0)*x^3/3!+cos(0)x^5/5!-...

=x-x^3/3!+x^5/5!-x^7/7!+....

So the given expression removes the first two terms of the expansion:

sin(x)-x+((x^3)/3!)

=x-x^3/3!+x^5/5!-x^7/7!+.... -x+x^3/3!

=x^5/5!-x^7/7!+....

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