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(35S) Limit of a function: LIM x→c+ and LIM x→c-
02-20-2022, 01:48 PM (This post was last modified: 03-29-2022 01:42 PM by Roberto Volpi.)
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(35S) Limit of a function: LIM x→c+ and LIM x→c-
This short program computes the limit for x approaching to a value, from both the right and the left, of a function previously stored in the Label F with x as unknown.


001 LBL L
002 1 E -9
003 F1?
004 +/-
005 STO +x
006 XEQ F
007 F0?
008 RTN
009 2 E -9
010 STO -x
011 R down
012 XEQ F
013 x<>y
014 RTN


Select Mode RAD in case of trig function;
Input a function with "x" as unknown, EQN or RPN format alike, in LBL F, followed by RTN;
press XEQ L;
input x value;
press R/S.

in a few seconds, you will have the results as follows:

STACK y: Limit from the left
STACK x: Limit from the right

In case it is used as subroutine for longer programs, or you need to use the "FN=" instruction, set flag 0 if you need just the limit from the right, or set flag 1 if you need just the limit from the left.

In case the result is approaching to +∞ or -∞, the result may be represented by a high number, millions or mantissa+exponent.

It could not work for very nasty functions, as the infamous "Lim x→0 of [1/sin^2(x) - 1/x^2]" specifically elaborated by the late Prof. James Stewart in "Lies my Calculator and Computer Told me", but it does a great job most of the times.


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