Tuesday

March 3, 2015

March 3, 2015

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

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 11:43pmA 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!+....

**Answer this Question**

**Related Questions**

Math - Hello, I am learning about Taylor series in school, but they are quite ...

Calculus - Taylor #2 - Find the Taylor series for f(x) centered at the given ...

Calculus - Please.... I need your help! I posted this question yesterday and no ...

calculus-- need help desperately! - The Taylor series about x=5 for a certain ...

Calculus - Obtain the MacLaurin series for 1/(2-x) by making an appropriate ...

Calculus Derivative- Taylor Series? - let f(x)= x/x-1 find f'(x) f ''(x) and a ...

Calc 2 taylor series - use the definition of a taylor series to find the Taylor ...

Taylor seires - f(x) =ln (1-x) a) Compute f'(x), f''(x), f'''(x). Spot the ...

Calculus - Hi~ Thank you for your help! I was trying to work on a problem about ...

Calculus!!! - I need your help... I've posted this question a while ago but no ...