# Math Help - Find my error

1. ## 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 $x^2(x-\sin(x))^2$

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

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

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

Where am I going wrong?

2. Hello,

I may be stupid but :

Originally Posted by Mathstud28
I am doing a limit and I must expand this using power series
Did you decide it ?

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

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

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