Symbolic limit of a function of 2 variables, HP49/50 « Next Oldest | Next Newest »

 ▼ Gilles Carpentier Senior Member Posts: 468 Threads: 17 Joined: May 2011 08-26-2012, 10:28 AM HI, Here is a program for HP49/50 whch try to find the lim (X,Y)->(a,b) of a function of two variables. Just put your function on the stack (variables must be X,Y) , and the { a b } limit you search. You will see in return : ```lim:number is the limit found by the program lim: oo (infinite limit) lim:? no limit found lim: f(t) no limit, the function returned is the limit in function of t, the angle of approach. Must be in RPN and exact mode. Be careful about X Y r t not define as global variables. If you try it, you will see some limitations but in most cases it works fine. « {'X' 'Y'} DUP ROT ADD = + « SUBST » STREAM DUP 'X=0' SUBST 'Y=0' SUBST IF EVAL DUP '?' SAME THEN DROP 'X=r*COS(t)' SUBST 'Y=r*SIN(t)' SUBST SIMPLIFY IFERR 'r=0+0' lim THEN DROP2 '?' END ELSE NIP END SIMPLIFY 'Lim' ->TAG » 'LimXY' STO For example : '3*X^2*Y/(X^2+Y^2)' { 0 0 } LimXY. Here you get : lim:0 '(X^2-Y^2)/(X^2+Y^2)' {0 0} Lim: '-(2*SIN(t)^2-1) that means no limit (as the limit depands of the angle to approach the point). You can modifiy this if you prefer with '?' and no detail 'X*SIN((X+Y)/4)' { 'PI' 'PI' } Lim:PI 'LOG(X+e^Y)/Sqrt(X^2+Y^2)' { 1 0 } Lim:LOG(2) 'LN(X+Y)/(X^2+2*X*Y+Y^2-1)' { 1 0 } Lim:1/2 '(X^2*Y^5)/(X^4+X^2*Y^2+Y^4)' {0 0} Lim : 0 '8*(X^2*Y^2)/(X^4+Y^4)' {0 0} Lim: '-((8*SIN(t)^4-8*SIN(t)^2)/(2*SIN(t)^4-2*SIN(t)^2+1))' @ Mean the limit does not exist SIN(X+Y)/(X+Y) { 0 0 } Lim: 1 ' (X^2+Y^2-2*X-2*Y)/(X^2+Y^2-2*X+2*Y+2)' { 1 -1 } Lim: oo (infinty) ' (X^3+X*Y^2)/(X^2+Y^2)' { 0 0 } Lim : 0 etc. ``` Edited: 26 Aug 2012, 10:34 a.m.

 Possibly Related Threads... Thread Author Replies Views Last Post HP50g: Writing a function that returns a function Chris de Castro 2 679 12-10-2013, 06:49 PM Last Post: Han HP: Dump the predefined variables! bluesun08 12 1,217 11-19-2013, 02:18 PM Last Post: bluesun08 HP Prime suggestion to avoid Numeric/Symbolic confusion Chris Pem10 4 656 11-19-2013, 05:49 AM Last Post: bluesun08 HP Prime... NOT meant to replace HP48,49,50 ? Chris Pem10 21 1,850 11-18-2013, 03:30 PM Last Post: Chris Smith HP Prime - local variables retain their initial type BruceH 4 658 11-10-2013, 12:42 PM Last Post: Michael de Estrada Shutdown with the Apps key and more than 10 variables in a program. Davi Ribeiro de Oliveira 10 1,239 11-05-2013, 01:26 PM Last Post: Han HP Prime: Number of external Variables Davi Ribeiro de Oliveira 0 337 11-01-2013, 08:10 PM Last Post: Davi Ribeiro de Oliveira HP Prime variables Davi Ribeiro de Oliveira 3 530 10-31-2013, 02:24 AM Last Post: cyrille de Brébisson HP Prime - deleting variables bluesun08 1 384 10-29-2013, 06:36 PM Last Post: Joe Horn HP Prime: CAS Variables - -How to save? Helge Gabert 2 499 10-27-2013, 11:26 PM Last Post: Helge Gabert

Forum Jump: 