Answer: The data for Exercise 5 were generated using the following functions. Use the

Step 1 of 8

First, let's find the error bound for the given function using the result of Theorem ,

We will need the second derivative of  in case , and also the third derivative for the case when . It is simple to determine the derivatives as follows.

Let's observe the case when . On the interval , the second derivative is a positive, strictly decreasing function, therefore its maximum absolute value is at . Hence, the error bound for the approximation  of  is

The true error of the approximation in the solution to Exercise 5 is

Which is indeed by absolute value smaller than the bound above.