Homework Five: Due 15 October, 2010



Proof by Induction:

  1. Use proof by induction to prove the power rule for differentiation. In your proof, make use of the product rule and the fact that the derivative of x is 1. (Note: There are many examples of this proof online. But give it a try yourself and ponder it for a bit before you google it.)
  2. Prove that for all natural numbers n, 6 divides n^3 - n. (Problem 3.2.4 from Chapter Zero: fundamental Notions of Abstract Mathematics, Carol Schumacher, Addison-Wesley. 2001.)

Chapter 2.4:

  1. 33

Chapter 2.5:

  1. 5 (a)-(c)
  2. 8 (a) and (b)
  3. 12
  4. 14
  5. 17
  6. 20
  7. 21

Chapter 2.6:

  1. 1
  2. 4
  3. 10
  4. 12 (a) and (b)