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RE: [apcalculus] e
Posted:
Oct 23, 2012 5:31 PM


NOTE: This apcalculus EDG will be closing in the next few weeks. Please sign up for the new AP Calculus Teacher Community Forum at https://apcommunity.collegeboard.org/gettingstarted and post messages there.  Calculators and computers are only able to carry a certain number of decimal places (I believe the TI calculators compute with 14 places and round to 12  something like that). Once past that number the calculator is rounding the (1 +1/x) to 1. Hence the expression looks to the calculator like 1^x. You can see this by calculating (1 + 1/x) for x = 10^12, then 10^13, etc.
It is a "fault" of the technology.
Lin
Lin McMullin Richardson, TX
My Blog for calculus teachers: teachingcalculus.wordpress.com
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> Original Message > From: erinslong@yahoo.com [mailto:erinslong@yahoo.com] >  > So I had a pre calculus student ask me why the lim x>inf (1+1/x)^x is e. I can > prove it, but I've never noticed until he showed me this that in the calculator, > the graph of (1+1/x)^x actually goes to one when you plug EXTREMELY large > numbers into the table values. Does anyone know how to explain this? > > Greatly appreciate your thoughts! >
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