Homework, due 1/28:

1.

Using the definition of limit, verify that if $f:(-\infty,\infty)\rightarrow(-\infty,\infty)$ and f(x) = x³, then $\lim_{x\rightarrow 2}f(x) = 2^3$.

2.

Verify that the funnel principle (Pinching Theorem) holds for limits: If f, g and h have a common domain, $h(x) \leq g(x) \leq f(x)$ and

$$\lim_{x\rightarrow a}f(x) = b = \lim_{x\rightarrow a}h(x)$$

then

$$\lim_{x\rightarrow a}g(x) = b.$$

3.

Complete the following exercises on pages 87-89 of Stewart: #2, #6, #14, #32, #38.