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Can you figure out the movie title? TEACHING CALCULUS USING MOVIES AND TELEVISION SHOWS Elana Reiser St. Joseph’s College, NY [email protected] Solution Snakes on a Plane! Example 1: Infinity What is up with infinity? Is infinity a number? What is ∞+1? What about 2 ∙∞? What about ∞ ∙∞? . Still not convinced? Infinity divided by infinity doesn’t equal one Assume it does FAIL Revenge It gets weirder There is more than one kind of infinity Countably infinite Integers Uncountable Real numbers between 0 and 1 Activity True or False: There are more numbers between 0 and 2 than there are between 0 and 1. Solution FALSE There are the same amount of numbers between 0 and 1 as there are between 0 and 2 The Fault in Our Stars Example 2: Zeno’s Paradox History Zeno of Elea Greek philosopher Wrote book of paradoxes According to Aristotle, invented style of debate where one person presents an idea and another reduces idea to absurdity earliest form of proof by contradiction History IQ Activity Activity Example 3: Limits Mean Girls The Problem Activity In level of increasing difficulty Plot function and explain why limit DNE Plug in values to right and left of zero to explain Evaluate using L’Hopital’s Rule If the minus sign between natural log and sine term changed to dot for multiplication the answer is -1 2 applications of L’Hopital’s Rule with product rule and quotient rule Activity First L’Hopital’s Activity Second L’Hopital’s with product rule and quotient rule Example 4: Derivative The Simpsons Activity Example 5: Area of Ellipse Rushmore Rushmore Rushmore True Story Something similar happened to George Dantzig As graduate student at Berkeley arrived late to class and saw problems written on board handed in correct solutions later found out they were actually two famous unsolved problems in the field of statistics Activity Example 6: Geometric Progressions The Big Bang Theory Activity Given data n 0 1 2 3 Y (days) 27 2 3 hours 20 minutes n 0 1 2 3 Y (days) 27 2.25 .1875 (4.5 hours) .015625 (22.5 minutes) Is there a better model? Activity n 0 1 2 3 Y (days) 27 2 .148 (3.5 hours) .01097 (15.8 minutes) Questions? [email protected]
