Solutions to Problem Set 18

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

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