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)xcos(0)*x^3/3!+cos(0)x^5/5!...
=xx^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!)
=xx^3/3!+x^5/5!x^7/7!+.... x+x^3/3!
=x^5/5!x^7/7!+....