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?

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.