00:01
So we're going to find the third, or actually, sorry, the fourth taylor polynomial of our function, natural log of x.
00:09
About x is equal to 1 or a is equal to 1, it's the same thing.
00:14
So we're going to have to find the first four derivatives of our function.
00:17
So the first derivative is just 1 over x, natural log of x.
00:21
That's just the derivative of the natural log of x.
00:25
The second derivative is going to be negative 1 divided by x squared.
00:30
The third derivative.
00:33
It's going to be 2 divided by x to the third.
00:37
And the fourth derivative, it's going to be negative 6 divided by x to the fourth.
00:45
And i just use the power roll to find each of these derivatives.
00:49
Since 1 divided by x is equal to x to the negative 1 power, so we bring down the power and we minus one of the power, and that's what i did with each of these derivatives.
00:58
So now we want to figure out what these derivatives, as well as our original function is equal to at 1...