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

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

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

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?

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?

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

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 691-92: 5, 12, 33