If I first delete the output I have the same result. It seems to happen when I copy text from within a section of one worksheet and paste it to another worksheet. If I copy Maple input only, it seems to work; If I include only text (or text with Maple input), Maple crashes. Thanks for your previous reply.

I am exploring two conceptual models of how students understand functions: as processes and as objects. The piecewise construct promotes a view of mathematical functions as discrete objects whereas a procedural construct promotes the view of a function as a process. I agree that the piecewise construct is certainly more concise and closer to standard mathematical notation, however, I am interested exploring how these different models promote (or fail to promote) certain mathematical understandings. Thanks very much for your response; I appreciate your input and suggestions. Chris de Castro

Note: So as to not "seriously" alter the derivative of the function (by adding a high frequency component) it works better to use a simple linear function with a "small slope." i.e. evalf( Limit( 1+10.0^(-15)*x, x=1, left) );

Note: So as to not "seriously" alter the derivative of the function (by adding a high frequency component) it works better to use a simple linear function with a "small slope." i.e. evalf( Limit( 1+10.0^(-15)*x, x=1, left) );

I was able to make a workable solution thanks to your comment about the behavior of evalf(Limit(k(x),x=1,left) for contant functions k(x). I simply added a "tiny" sin function of small amplitude and high frequency to the desired constant. Now to the precision of evalf, I get the correct answer. The plots look alright as well. Thanks. evalf(Limit(1+10^(-20)*sin(10^20*x),x=0,left)) --> 1

I was able to make a workable solution thanks to your comment about the behavior of evalf(Limit(k(x),x=1,left) for contant functions k(x). I simply added a "tiny" sin function of small amplitude and high frequency to the desired constant. Now to the precision of evalf, I get the correct answer. The plots look alright as well. Thanks. evalf(Limit(1+10^(-20)*sin(10^20*x),x=0,left)) --> 1

I really appreciate the time you have put into this question! I wonder whether the copy of Maple that I am using (provided by my school system) has some early libraries that have some idosyncratic bugs. Do you know if it is possible to find copies of the maple 8 library files (in Maple/lib) that I might try replacing? I will look on the Maplesoft site but I suspect that it's so old that I'll not find anything. Thanks! Chris

This is the worksheet I have been working with. You can see the output that Maple 8 provided me. Of course it's not magic but as Arthur C. Clark puts it "any sufficiently advanced technology is indistiguishable from magic." Thanks for your help :) Chris Download 2060_LimitOfProcedure.mws
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I appreciate your help. My students will be using Maple 8. I would like to understand how to utilize functions defined by procedures in the same manner as functions defined piecewise (with the possibility of conditional expressions within the procedure). Do you know if there is something about the way Maple internally utilizes series to evaluate limits that leads to a limitation such as we are seeing? Thanks! Chris

When I try your suggested code I get limit('k(x)',x=1,right) ---> 1 limit('k(x)',x=1,left) ---> k(1) I don't see any major difference between your code and what I wrote in my original post, yet the result is slightly different. In this case, at least I get one of the two one-sided limits correctly. Can you explain the difference? Thanks for your reply! Chris

Thank for your reply. It is appreciated. When I tried this in Maple 8, I still had the same result. What I am attempting to do is take a procedure and create a function from the procedure to which I can apply the limit procedure; I believe the process you are suggesting is the reverse process. Thanks again! Chris de Castro