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.

$\lim_{x \to 1} 2x - 3 = -1$
$\lim_{x \to 2} \frac{x^2 - 4}{x-2} = 4$
$\lim_{x \to a} 3x + 2 = 3a + 2$ for all $a \in \mathbb R$ .
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 $n = 0$ .