00:01
In this question, we choose the function if to be 1 minus x to the minus 1 .5.
00:09
And we use the tailor polynomial pnx centered at a equals 0 to approximate the function f.
00:24
So in fact, what we want to do is we want to find an approximation for approximate for a for 0 .15.
00:42
So let's take a couple derivatives first.
00:46
So the first of the derivative equals to one half, one minus x to the three half, minus three half.
00:52
The second the derivative is three over four, one minus x to the minus five half.
00:59
Third of the derivative equals to 15 over eight, one minus x to the minus seven half.
01:07
And we plug in the center into all of these functions.
01:11
So f0 equals to 1.
01:13
F prime 0 equals to 1 half.
01:16
Second order derivative is 3 over 4.
01:20
Third order derivative equals to 15 over 8...