Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Courses » ap-calculus

Topic: [ap-calculus] e
Replies: 1   Last Post: Oct 23, 2012 5:44 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View  
Jon Stark

Posts: 914
Registered: 6/10/06
RE: [ap-calculus] e
Posted: Oct 23, 2012 5:44 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

NOTE:
This ap-calculus 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/getting-started
and post messages there.
------------------------------------------------------------------------------------------------
Your calculator simply doesn't keep enough digits.
Pick a big x value, such as 10 ^ 15. The exponent will be represented properly in the calculator something like 1.000000000000 E 15, keeping 12 (or perhaps 14, depending on model) significant digits in a form equivalent to scientific notation.
But the part of your expression in parentheses is (1 + 10 ^ (- 15)) which must be computed by addition.
To get that value, the calculator tries to add 1.00000000000 to .000000000000001 (represented internally as 1.00000000000 E 0 and 1.00000000000 E -15), which SHOULD be 1.000000000000001. Note that the final "1" is very, very far from the leading "1" in that sum. Since the calculator can't keep more than 12 digits, it truncates that down to 1.00000000000 and your expression is really evaluated as just (1) ^ (10^15) instead of the computation you meant to do, so the result will obviously and erroneously approach 1.
If your calculator could keep an enormous number of digits, you could get answers approaching e with larger x values, but eventually you would reach a point at which the sum would truncate as above.

Erinslong asked:
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?

________________________________

This electronic mail transmission and any files transmitted with it may contain confidential information only for use by the intended recipients. Unless you are the addressee (or authorized to receive messages for the addressee), you may not use, copy, disclose, or distribute this message (or any information contained in or attached to it) to anyone. If you received this communication in error, please notify the sender by reply e-mail and then delete the communication from your electronic mail system.

---
To search the list archives for previous posts go to
http://lyris.collegeboard.com/read/?forum=ap-calculus



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.