The Maclaurin series for
is given by
. This series represents the expansion of
around the point x=0 using the derivatives of the function at that point. The series includes terms for all non-negative integer values of n. The general term in the series is

The Maclaurin series expansion for
can be obtained by substituting the given hint into the function. The Maclaurin series for
can be expressed using the hint as follows:

Now, substitute this into the original function
:

Now, let's express cos(2x) as a Maclaurin series. The Maclaurin series for cos(x) is well-known:

So, for cos(2x):

Now, substitute this into the expression for f(x):

To obtain the Maclaurin series for f(x), you can distribute the 9/2 and simplify the expression:

So, the Maclaurin series for
is
