## Practice Problems

Work through the odd-numbered problems 1-23. Once you have completed the problem set, check your answers.

### Answers

1. (a) If is within unit of 3.

3. (a) If is within unit of 2.

5. Problem 1: slope Problem 3: slope .

General pattern: slope for linear functions

7. Each board must be within inches of 10 inches in length.

13. Each piece of wire must be within inches of 5 inches.

15. & 17. See Figures

There is no value of that is both larger than and smaller than so the limit does not exist.

21. Take (or smaller) and suppose is within 1 of .

There is no value of that is both larger than and smaller than so the limit does not exist.

23. This proof is very similar to the proof of the second theorem on page 9.

Assume that and . Then, given any , we know and that there are deltas for and and , so that

if , then ("if is within of a, then is within of ", and

if , then ("if is within of , then is within of M").