The data in Exercise I were taken from the following functions. Compute the actual

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To get the actual errors and error bounds from the indicated exercise, we need to evaluate the forward difference formula for   and backward-difference formula for   where   is the linear difference between   's to get the approximation for   approx given the tables.

After getting the approximation for  , we can calculate the actual error by getting the derivative of the given function  , and subtract it with the approximation we've obtained in the specified exercise.

We can present the actual error as;

For the error bound, we can use the formula   where   is a bound on   where  . To understand it easier, we just need to get the 2 nd derivative of   and substitute a value to that second derivative that is within   and  .