Texas Instruments TI89 and TI92 Plus Computer 



Version  1.2 (Thursday, September 23, 1999) 
Download  [ lim.89f  lim.9xf ] (906 bytes) 
Description  Determines multivariable limits.
1.1: Added the ability to indicate left or right limit for each variable. 1.2: Added some tests that will eliminate some but not all undefined limits. 
Screen shots 

Documentation  Usage:
lim(expr,VarList,LimitPoints) expr: An EXPR of zero or more variables. VarList: A LIST of the limit variables. LimitPoints: Can be type NUM, LIST, or MAT:
NOTE: This function calls the builtin limit() function n^{2} times, where n is the number of variables in VarList, so each additional variable in the expression will significantly add to the amount of time it takes to evaluate it. The reason for this is that I cannot come up with a routine that will prove or disprove a limit so I try to eliminate some invalid limits by changing the order in which variables are evaluated. Ideally this would be n! evaluations so n^{2} is a compromise. Return Value:
Example:
. lim(x^{2}y/(x^{4}+y^{2}),{x,y},{0,0))y=x^{2}
3. lim(ln(x)+ln(y)+ln(z),{x,y,z},{0,0,0}) [Limit as (x,y,z)
> (0,0,0)]
lim(ln(x)+ln(y)+ln(z),{x,y,z},[0,1;0,1;0,1])
[Limit as (x,y,z) > (0^{+},0^{+},0^{+})]
