Wow! Thats amazing Robert. Your approach of using implicit plot with filled regions was exactly what I needed and the resulting plot verified what I had done by hand. I have to admit that i would never have thought of that approach. Many thanks. <=2

Wow! Thats amazing Robert. Your approach of using implicit plot with filled regions was exactly what I needed and the resulting plot verified what I had done by hand. I have to admit that i would never have thought of that approach. Many thanks. <=2

It's very frustrating but sometimes posting a message here doesn't include all that I type which I see in the message form, and this has again happened in this case. Why this is I don't know but that is another problem. What I tried to originally post was |x-y|+|x|-|y|less than or equal to two but the less than or equal to two symbols were left out of my post for reasons that I don't understand. In any case, I can't seem to find a way to plot this "inequality" using Maple.

It's very frustrating but sometimes posting a message here doesn't include all that I type which I see in the message form, and this has again happened in this case. Why this is I don't know but that is another problem. What I tried to originally post was |x-y|+|x|-|y|less than or equal to two but the less than or equal to two symbols were left out of my post for reasons that I don't understand. In any case, I can't seem to find a way to plot this "inequality" using Maple.

Thanks, but I can't seem to get this program to work with absolute values. Is there some way to get this plot program to work with absolute values? Perhaps I am at fault here and not using it correctly?

Thanks, but I can't seem to get this program to work with absolute values. Is there some way to get this plot program to work with absolute values? Perhaps I am at fault here and not using it correctly?

Thank you Mr. Schivnorr.

Thank you Mr. Schivnorr.

According to "Precalculus, Functions and Graphs" 10th edition by Sworkowski and Cole near the top of page 24 it says: If the cube root of "a" equals "b", then b^3=a. If I use x instead of a and y instead of b, the principle is restated as if y=x^(1/3) then y^3=x in which case y^3=x and y=x^(1/3) are equivalent statements. So when you say "lastly, y^3=x is not the same as y=x^(1/3)" I don't understand. They may not be in the same form but they are mathematically equivalent and should yield the same results when used in solve to find the cube roots of 1. I am not trying to argue, I just don't understand. Could you explain it more simply for a simple guy like me? (Thanks for the reply.)

According to "Precalculus, Functions and Graphs" 10th edition by Sworkowski and Cole near the top of page 24 it says: If the cube root of "a" equals "b", then b^3=a. If I use x instead of a and y instead of b, the principle is restated as if y=x^(1/3) then y^3=x in which case y^3=x and y=x^(1/3) are equivalent statements. So when you say "lastly, y^3=x is not the same as y=x^(1/3)" I don't understand. They may not be in the same form but they are mathematically equivalent and should yield the same results when used in solve to find the cube roots of 1. I am not trying to argue, I just don't understand. Could you explain it more simply for a simple guy like me? (Thanks for the reply.)

Yes, I tried solve(y = 1^(1/3), y); and only 1 was returned. Now I find that solve(y^3=1,y) gives all three roots. Why won't (y = 1^(1/3), y) return all three roots while solve(y^3=1,y) will?

Yes, I tried solve(y = 1^(1/3), y); and only 1 was returned. Now I find that solve(y^3=1,y) gives all three roots. Why won't (y = 1^(1/3), y) return all three roots while solve(y^3=1,y) will?

Thank you Doug for your reply. It causes me a new found respect for the power of Maple, along with some concern and a couple of new questions. If Maple routinely uses techniques like non-FTC approaches to evaluating integrals, there is some concern in my mind for accurate answers considering the possibility of software bugs. Namely if I don't understand what Maple is doing, I cannot check its results and even worse if Maple is using some proprietary method, the user in general will not understand what is going on and we end up with push a button and hope technology. Obviously the burden is on the user to upgrade his/her/ or my math understanding, if that will make such Maple results understandable so my next question is would it be likely that a course on complex variables as any quality college would cover non-FTC integration techniques? Also, what commonly available book explains non-FTC techniques in the most understandable manner. While I started out to to find out the how a difficult integral was achieved I ended up finding out that there is apparently a lot of math techniques that I am unaware of. So my next question is has anyone published a survey of math indicating what is covered in each particular subject. Lastly, I have to wonder if the body of knowledge for mathematics, like that for medicine, has become so large that it is necessary to specialize on one particular branch? Could you comment on that please. Hopefully you will find time to reply and I I want to thank you in advance for any effort you might make in that regard. Thanks Doug.

Thank you Doug for your reply. It causes me a new found respect for the power of Maple, along with some concern and a couple of new questions. If Maple routinely uses techniques like non-FTC approaches to evaluating integrals, there is some concern in my mind for accurate answers considering the possibility of software bugs. Namely if I don't understand what Maple is doing, I cannot check its results and even worse if Maple is using some proprietary method, the user in general will not understand what is going on and we end up with push a button and hope technology. Obviously the burden is on the user to upgrade his/her/ or my math understanding, if that will make such Maple results understandable so my next question is would it be likely that a course on complex variables as any quality college would cover non-FTC integration techniques? Also, what commonly available book explains non-FTC techniques in the most understandable manner. While I started out to to find out the how a difficult integral was achieved I ended up finding out that there is apparently a lot of math techniques that I am unaware of. So my next question is has anyone published a survey of math indicating what is covered in each particular subject. Lastly, I have to wonder if the body of knowledge for mathematics, like that for medicine, has become so large that it is necessary to specialize on one particular branch? Could you comment on that please. Hopefully you will find time to reply and I I want to thank you in advance for any effort you might make in that regard. Thanks Doug.

If you can figure out what the _B's really mean from the help page, please let us know. Every time I read it, I seem to come away more un- certain as to their meaning.