Math 310-01/02

10-23-2017

1. Prove that .

Let . Set . If , then

So

In the third step, the inequality is not reversed on division by , because implies .

This proves that .

2. Use the limit definition to prove that

Let . Set . Then

Suppose . Then

Using the second inequality,

In the last step, the inequality is not reversed, since implies . The latter implies that , so

This proves that .

*The earth keeps some vibrations going There in your heart, and
that is you.* - *Edgar Lee Masters*

Copyright 2017 by Bruce Ikenaga