# Question #0a436

##### 1 Answer

Maclaurin expansion to the 4th term:

And using this series to approximate

#### Explanation:

A Maclaurin series is just a Taylor series expansion of a function about 0:

In our case,

To get the other terms, of the series, we must compute derivatives of the function.

To get the first derivative, we should use the power rule

And to get the second term of the expansion, we evaluate the first derivative with

To get the second derivative, we take the derivative of the first derivative.

To get the third term of the expansion, we evaluate the second derivative with

To get the third derivative, we take the derivative of the second derivative.

To get the fourth term of the expansion, we evaluate the second derivative with

Thus, the Maclaurin series up to the fourth term is

Now, to approximate

and we plug