00:01
In this question, we are asked to find the maclaurin series for the given function, and write down the coefficients from c1 to c5.
00:09
First of all, recall that e to the u equals to the series u to the n divided by n factorial, and from 0 to infinity.
00:20
Then, replace u by negative 9x, and we'll get the series for the function f.
00:27
We'll get 6x squared multiplied by the series negative 9x to the nth power divided by n factorial, and from 0 to infinity.
00:42
This equals to 6x squared multiplied by the series negative 1 to the n multiplied by 9 to the n times x to the n over n factorial, and from 0 to infinity.
01:00
And finally, after moving 6x squared inside, we'll get the series negative 1 to the n multiplied by 6 times 9 to the n times x to the n plus 2 divided by n factorial, and from 0 to infinity.
01:18
Now let's write down the first few terms of the series.
01:24
For n equals 0, we'll get 6 multiplied by x squared...