The Maclaurin series of a function is simply the Taylor series of a function about a=0:

Because we were asked to find the first three terms (n=0 to n=2), we must find the zeroth, first, and second derivatives of the function. The zeroth derivative is just the function itself.

Now plug in  into the formula and write out the first three terms (n=0, 1, 2):

The Maclaurin series for any function is simply the Taylor series of the function about a=0:

We first must find the zeroth, first, and second derivative of the function (for n=0, 1, and 2). The zeroth derivative is the function itself:

The derivatives were found using the following rules:

, 

Now, we just use the formula, with , to write out the first three terms of the series (n=0, 1, and 2):

The Maclaurin series for a function is simply the Taylor series for the function about a=0:

We must find the first two terms of the series, corresponding to n=0 and n=1. We need the zeroth and first derivative of the function, the zeroth derivative being the the function itself:

The derivative was found using the following rules:

, , 

Now, use the formula above to write out the first two terms:

The Maclaurin series for any function is simply the Taylor series for the function about a=0:

First, we must find the zeroth through fourth derivative of the function. The zeroth derivative is simply the function itself.

The following rules were used for the derivatives:

, 

Next, we simply evaluate all of the derivatives at  and then write out all of the terms:

which simplified is equal to

The Maclaurin series is the Taylor series for a function about a=0:

We need to find the zeroth, first, second, and third derivative of the function (n=0, 1, 2, and 3). The zeroth derivative is simply the function itself.

The derivatives were found using the following rule:

Now, use the above formula, with  to write out the first four terms:

which simplified becomes

The Maclaurin series for any function is simply the Taylor series for the function about a=0:

For the first two terms (n=0, 1) we must find the zeroth and first derivative of the function. The zeroth derivative is just the function itself.

Now, using the above formula, write out the first two terms:

The formula for an i-th degree Maclaurin Polynomial is

For the fifth degree polynomial, we must evaluate the function up to its fifth derivative.

The summation becomes

And substituting for the values of the function and the first five derivative values, we get the Maclaurin Polynomial

The Maclaurin series for  is given by 

The Maclaurin Series for  is given by

Since the question asked

To write this sum, we can take out  as a common factor for both series: