1. Infinity and Beyond!
A prelude to Infinite Sequences and Series (Ch 12)

3. Infinity and Fractals…
Fractals are self-similar objects whose overall geometric form and structure repeat at various scales they provide us with a “glimpse” into the wonderful way in which nature and mathematics meet.
Fractals often arise when investigating numerical solutions of differential (and other equations).
… go to XAOS

4. Paradoxes of Infinity Zeno Motion is impossible
Achilles and the tortoise
Math prof version

5. The Koch Snowflake and Infinite Sequences…
What is a Koch Snowflake?
How “long” is a section of the Koch Snowflake between x = 0 and x = 1?
Anything else odd about this?
What “dimension” is it?
Can you differentiate it?

6. The Koch Snowflake and Infinite Sequences…
What is a Koch Snowflake?
How “long” is a section of the Koch Snowflake between x = 0 and x = 1?
Anything else odd about this?
What “dimension” is it?
Can you differentiate it?

7. What is the area of a Koch Snowflake?
Start with this…

8. Rules of the Game…
Section 10.2 – defines sequence and basic terminology
Use many of the ideas that you developed about limits in Math 200
Important Theorems:
The Squeeze Theorem
L’Hopital’s Rules (pg 692: 30,48)
Examples: pg : 5, 12, 33