00:01
All right, so we want to find the taylor series.
00:02
This is a little bit weird because this is a polynomial.
00:05
It's 1 plus x squared plus x cubed.
00:10
So if it was a tailor series centered around a equals 0, we'd be done because this is already a tailor series.
00:16
But it's centered around a equals 1.
00:17
So we want it as a polynomial expanded not in x, but in x minus 1's powers of x minus 1.
00:24
So we still need to do it.
00:25
We need to find three derivatives.
00:28
Luckily the derivatives will be nice.
00:31
First derivative is 2x plus 3x squared.
00:35
The second derivative is 2 plus 6x.
00:38
Third derivative is just 6.
00:40
And then i need to find those values at 1...