Re: calculating e Part II

To: CALC-TI@LISTS.PPP.TI.COM
Subject: Re: calculating e Part II
From: Justin Smith <smit811no1spam@TAO.SOU.EDU>
Date: Wed, 4 Mar 1998 17:59:51 +0100
Organization: -
References: <v01530500b1231626980f@[206.216.138.82]> <InmL.256$Ra4.292794@news2.atl.bellsouth.net>
Reply-To: Justin Smith <smit811no1spam@TAO.SOU.EDU>
Xref: paladin.american.edu bit.listserv.calc-ti:21255

HINT:

Graph (1+(1/x))^x  on your calculator. Also graph e.....not the function
e^x, but just the constant e if you can. (Not sure if it can be done on a
calculator other than the TI-92, but still try..)

After graphing....


Wow!! Look how close the e line is to the (1+(1/x))^x line!! (ie..that is
why the formula is a good approximation..). But observe what happens on
the right side of the axis..(you may need to zoom out A LOT, so the xmax
is 1E15 or so, then zoom in as needed..).

IN other words...(1+(1/x))^x isn't the best of approximations for e as x
increases.


>I wanted to know why the calculator
>>displays a number _greater_ than the approximation of e (e displayed to 9
>>decimals) when A is 10x10^13.

I have a TI-92, and when I ran your code at 1e14 my value for B
(approximation of e) went to 1! (the very far right side of the graph..)

Because [1+(1/1e14)^1E14] is like:
(1+0)^0


Hope that helps!

-Justin

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Follow-Ups:

Re: calculating e Part II

From: Rene Kragh Pedersen <u971168@DAIMI.AAU.DK>

References:

calculating e Part II

From: Lisa Ledwith <lledw@GA.K12.PA.US>

Re: calculating e Part II

From: Joe Horton <joehorton@USA.NET>