# Find my error

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• May 12th 2008, 03:02 PM
Mathstud28
Find my error
I am making a stupid error somewhere and its bugging me...help me find it please

I am doing a limit and I must expand this using power series and then cancel terms for $\displaystyle x^2(x-\sin(x))^2$

$\displaystyle (x^2-s\sin(x))^2$

So $\displaystyle x^4-2x^3\sin(x)+x^2\sin^2(x)$

$\displaystyle x^4-2x^3\bigg[x-\frac{x^3}{6}+\frac{x^5}{120}-...\bigg]+\frac{x^2}{2}\bigg[1-\bigg(1-\frac{(2x)^2}{2!}+\frac{(2x)^4}{4!}-...\bigg)\bigg]$

Where am I going wrong?
• May 12th 2008, 03:07 PM
Moo
Hello,

I may be stupid but :

Quote:

Originally Posted by Mathstud28
I am doing a limit and I must expand this using power series

Did you decide it ?

Quote:

and then cancel terms for $\displaystyle x^2(x-\sin(x))^2$
What is the limit of x ?

Quote:

$\displaystyle x^4-2x^3\bigg[x-\frac{x^3}{6}+\frac{x^5}{120}-...\bigg]+\frac{x^2}{2}\bigg[1-\bigg(1-\frac{(2x)^2}{2!}+\frac{(2x)^4}{4!}-...\bigg)\bigg]$

Where am I going wrong?
What's going wrong ? Try to develop... And group the terms :/