1. MAT 3749 Introduction to Analysis Section 2.3 Part I Derivatives http://myhome.spu.edu/lauw

2. Preview Differentiable implies continuous Something else

3. References Section 2.3

4. HW Do not use ε-δ.

5. Derivatives

6. Example 1

7. Theorem

8. Analysis: Step 1

9. Analysis

19. Proof

23. Remark The converse of the last theorem is false

24. Example 2 Give a counterexample of the converse of the last theorem.

25. The Derivative as a Function

26. Change of Variables in Limits “Change of variables” is a technique you have used frequently to evaluate limits in a completely natural way. To formulate this technique formally and justify it rigorously, however, is a task requiring some subtlety.

27. Example 3

28. Classwork