Epsilon – Delta Definition of a Limit

Read pp. 31-32 Precise Definition of a Limit

1) Write Definition 4 (p.31) and Sketch Figure 13 (p.32) in your notes.

2) Write out complete definitions for left and for right limits. See the paragraph before Example 10.

3) Write out the proof for Example 9 in two parts A) find a formula for delta B) show that this delta works.

4) Write out the proof for Example 10 in two parts A) find a formula for delta B) show that this delta works.

Read pp. 64-66 Precise Definitions (of limits involving infinity)

1) Write Definition 6 and Sketch Figure 16. Does delta depend on M or does M depend on delta?

2) Write Definition 7 and Sketch Figure 17. Does epsilon depend on N or does N depend on epsilon?

3) Write Definition 8 and Sketch Figure 20. Does M depend on N or does N depend on M?

Read Appendix B pp. A10-A13 (not Theorem 3)

State each law separately and Write out its proof.

1) Triangle Inequality

2) Limit Law 1 (Limit of a sum)

3) Limit Law 4 (Limit of a product)

4) Limit Law 3 (Limit of a constant times a function)

5) Limit Law 2 (Limit of a difference)

6) Limit Law 5 (Limit of a quotient)

If you have any time left work on homework problems 23,26,33,43 from 1.3