Answer:
Step-by-step explanation:
In order to find this Maclaurin series, we can start by using a known Maclaurin series and modify it according to our function. A pretty regular Maclaurin series is the cos series, where:
So all we need to do is include the additional modifications to the series, for example, the angle of our current function is: so for
the modified series will look like this:
So we can use some algebra to simplify the series:
which can be rewritten like this:
So finally, we can multiply a 14x to the series so we get:
We can input the x into the series by using power rules so we get:
And that will be our answer.