00:01
In this problem, we are going to find the fifth degree taylor polynomial approximations for the functions sine x, cosine x, and exponential x centered around the origin, namely x equal to zero.
00:15
So these are well -known functions, so we can just write down the results.
00:23
We have cosine x equal to, we will have only the even powers, so x to the power zero, two, four, etc.
00:32
And the sign will be alternating, so one minus one over two factorial x squared plus four factorial x to the power four minus one over six factorial x to the power six plus and so on.
00:50
So to the fifth order, we have one minus one over two x squared plus one over twenty four x to the power four.
01:03
We don't have the fifth term because this is an even series in powers of x, so we have to leave it this.
01:19
In the second part, we have sine x...