Error Analysis Using Excel for E Series Worksheet Paper

Error Analysis This is very similar to example 3.8 in the Chapra and Canale textbook. Use Excel to implement an infinite-series approximation of e* as follows: 3 ex=1+x+ x2 + + 2! 3! n=0 n! Your worksheet will have 3 columns for each value of x: n, term to add, and approximation, which is the sum of all previous terms up to that point. Use n up to 35, and find the answer for x = 15,-1, and -15. Label the worksheet “double precision”, since Excel works in double precision mode by default. Now repeat the work using less precision: Create two new worksheets, “8 digits” and “5 digits”. The terms to be added are now kept to 8 digits and 5 digits in their respective worksheets. To do this, use the “rounddown(number,8)” and “rounddown(number,5)” in their respective worksheets. “number” is the expression you used for the term to add column in the double precision worksheet. The Rounddown() function is basically a truncation after the gth (or 5th) digit. This artificially introduces rounding errors similar to those introduced when smaller numbers of bits are used to represent the number. Once you have completed the 3 worksheets, copy your answers for the approximation at n=35 to a table in a new worksheet labeled “results”. The table will have the columns: x, true value, double precision approx., 8 digit approx, and, 5 digit approx, with row entries for x=15,-1, and 15. Also, beneath the -15 row, place a row that shows the value found for e’ in each case, raised to the 15th power. Include a brief discussion of your results as an added comment box. Why is the e-15 value the worst in terms of how well the 8- and 5-digit approximations work? Is it more accurate to use (e-l)* when a negative x is encountered? Why or why not?

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