Given: A function

Required: To approximate the value of the function when x=1 using the first six terms of the Maclaurin expansion.
Explanation: Maclaurin's expansion is a special case of Taylor's theorem. The terms of the expansion are as follows:

So we need to find the following terms at x=1

Further

We can write the given function as

The series would be

Solving further at x=1 gives

Hence the required function is-

Now for x=1 we have

Which gives

Final Answer: 8.93606