M2160-1 5^{th} Homework Assignment Due Mar. 24, 2006. |
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Do TWO out of three of the following problems.
A positive integer is called perfect if σ(n)=n. So the sum of the proper divisors of a perfect number equals the number itself. 6 is a perfect number because σ(6)=6. Can you find any other perfect numbers?
where a = 0.xxx is a decimal number (xxx represent the last three digits of your student id number). Use either bisection or Newton's method. Describe in detail the procedure you used to find the answer. Be sure to explain how you know that you've found all the solutions. Enclose the programs and the final result.
where a = 0.xxx is a decimal number (xxx represent the last three digits of your student id number as in problem B). Your explanation should justify the number of intervals you choose to compute your answer. You may use the error estimates for the trapezoid or Simpson's rules given in your calculus text [Varberg, Purcell & Rigdon, Calculus, 8th ed., Prentice Hall, 2000, section 11.2.]
E-mail your solutions to treiberg@math.utah.edu.