00:01
Hello.
00:02
So here we have the function f of x is equal to sine of x.
00:05
Now we want to find the mclaurin polynomials of orders 1, 2, 3, and 4 for f of x and then plot these on the same axes.
00:13
So using our definition for the p sub n of x, right, going up to the nth derivative evaluated at 0 over n factorial times x to the n.
00:24
So we first take our function and evaluate at zero.
00:29
So f of zero is just equal to sign of zero, which is equal to zero.
00:36
Now the first derivative here is cosine of x.
00:38
So the first derivative evaluated at zero is just cosine of zero, which is equal to one.
00:44
And then our second derivative at zero.
00:48
So the second derivative is going to be equal to negative sign of x or negative sign of zero is still zero.
00:55
So the second derivative at 0 is equal to 0.
00:58
The third derivative is then equal to negative cosine of x...