CC MATHEMATICS   MATHEMATICAL EXPLORATIONSSYLLABUS

Homework 5: Due Monday 9/25 at 4PM
Extended to Tuesday at 1 PM

Turn in individual solutions. You may work together in solving the problems, or get help from others, but the final write-up should be your own. Show full work for full credit. Do not turn in anything you cannot explain completely.

Part I: From Schaum's Calculus  Problem Further instructions
Problems on the IVT Use the IVP to show that x^3 - 3x + 1 has a root on the interval (0,1)
  Use the IVP to show that x^2 = (x+1)^1/2 has a solution on the interval (1,2)
Chapter 13 17b, 22  
Chapter 23 6c  USE THE FULL RIEMANN SUM LIMIT METHOD
  9, 11, 13  
Chapter 22 22, 24, 28, 34, 51, 60, 62, 65, 68  
Chapter 24 11, 17, 21, 38  
Chapter 29 10, 12b, 12f  
Chapter 30 14a 14b 27 47  

 Part II: Chaos Problem
Click HERE

 

 Bonus  Problem
Look at this "Sierpinski gasket" approximation for n = 0, n = 1, n = 2, n = 3, n = 4. For each n (general value, not just 1 to 4) find the area. Also, what is the area in the limit as n goes to infinity? (Suppose the largest triangle has side of length 1.)