Homework # 3

The following problems are for HW #3, which is due this Thursday, January 18th.

For the first three problems use \epsilon - \delta to show the following limits are true.

  1. \lim_{x \to 1} 2x - 3 = -1
  2. \lim_{x \to 2} \frac{x^2 - 4}{x-2} = 4
  3. \lim_{x \to a} 3x + 2 = 3a + 2 for all a \in \mathbb R.
  4. Prove for contradiction that the following limit does not exist: \lim_{x \to 0} \frac{1}{x} + x^2.

The rest of the problems are from the textbook.

Chapter 4: 17

Chapter 5: B. 14, 15

Chapter 6: A. 6, 14

EXTRA CREDIT: Following the problem with the last homework, let me be clear that (in this class) 0 counts as a natural number! For extra credit, give an example of a property of natural numbers n that is true for all n > 0 but false for n = 0.

Please let me know if you have any questions.


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