Section 1.1 (calculus review) Worksheet:

Assignment: Pages 15-: 1b,c; 2a,b; 3b; 4b,d; 5; 6; 9; 11; 12; 19; 20; 24; 26 (due Wednesday, 8/31).

  1. Definitions 1.3 mentions complex numbers: how are they represented? What is tex2html_wrap_inline169 for complex numbers?

  2. Give an example of function continuous everywhere, but not differentiable everywhere.

  3. Give an example of function not continuous anywhere!

  4. How can we use Rolle's theorem to prove the Mean Value Theorem?

  5. Use 1.10 to prove that

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  6. How can the Intermediate Value Theorem fail if the function f is not continuous?

  7. RE 1.11: What can go awry if g is allowed to change sign on [a,b]? Do we need that stipulation?

  8. Explain the Generalized Rolle's Theorem in the case when n=2.



Wed Aug 24 01:48:43 EDT 2005