This is a \"centered\" nite difference because we evaluate f at two points centered on either side of 1:. For brevity, people often refer to formulas (2) and (3) as simply a \"one-sided difference\" and a \"centered difference,\" omitting the word \"nite.\" A centered difference is the average of a one-sided difference based on x + As: and another based on a" 7 Am gives the centered difference formula; that is, %(OD(f, Art) + 0D(f, 7A$)) : OD(f, Am) (4) Question 1. In general, a centered difference is more accurate than a one-sided difference when approximating a derivative. Let's check that statement for a particular case: f (w) = sin :13. Make a table with ve columns: 9:, f(m) = sinzr, 5% = cos 2:, OD(f,A:c), OD(f,A3:). Fill column 1 with a: = 0,0.171,0.27r, . . . , 0.5%, and evaluate columns 2 through 5 for the specied values of :5. Write your answers with three decimal places. If you use a calculator, remember to set it to radians (and reset it to degrees when you are done). A better way to evaluate this table is to enter formulas into a spreadsheet. The values in column 2 do not provide the values needed to evaluate the last one-sided difference and the rst and last centered differences, so you will need to leave those entries empty. With a spreadsheet, you can include more values of (E with no more work on your part other than copying formulas into the extra rows, but you will always lack the last value of the one-sided difference and the rst and last values of the centered difference