Re: Various notes about the TI 92
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Paul Pollack (paulp@televault.com) wrote:
: James Rankin wrote:
: >
: > Richard Gallagher wrote:
: > > The TI-92 gives a incorrect result for the limit of 0^x as x tends
: > > toward 0. It gives the limit as 1 from the left, right and both
: > > sides. In fact the limit is 0 from the right, no limit from the left
: > > and hence no limit from both sides. It does give a 0^0 replaced by 1
: > > warning, but that does not really make up for it.
: >
: > Are you sure? I believe lim x->0 (0^x) is 1.
: Look at the values of the function at x>0. All of these values are 0;
: therefore, the limit from both sides can't be 1, regardless of
: what the limit from the left is.
: I'm sure this was probably just a silly mistake -- believe
: me, I make my own all the time [like spelling "theory" wrong in a previous
: post].
My guess is that the 92 probably tries substitution first and it
comes up with 0^0 which is often defined to be 1 to make certain
formula prettier.
Aaron
: Here's something else you may also want to try on the 92:
: 1. Evaluate 1/0 -- you should get undefined
: 2. Evaluate 0^2
: 3. Evaluate 1/ans(1)
: 4. Stare in horror as your 92 reports infinity
But 0^2 is a positive zero, you see. It makes a weird sort of
sense, really. Lim x->0 of 1/x^2 = +oo, for example.
: Shameless plug: Looking for number theory programs (yes, I didn't
: type "theory" wrong this time) for your TI-92? Ver 0.7 of my
: number theory program group should be available and now includes an
: implementation of pollard's p-1 method of factoring. Also:
: Pollard, that hideous program, is now a function (rho) that returns a much
: prettier string.
Why not implement RSA? :)
Aaron (Totient functions are your friends)
<pre>
--
Aaron Bergman -- abergman@minerva.cis.yale.edu
<http://pantheon.yale.edu/~abergman/abergman.html>
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