alla

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These are replies submitted by alla

 

 

 

 

 

 

 

 

 

 

 

I want to plot y = x^(2/5), so I tried

 

 

 

use RealDomain in

   plot(x^(2/5), x = -1..1,y = -1..1);

end use;

 

This works OK.

 

But if define

 

     f36 := x -> x^(2/5);

 

Then

 

use RealDomain in

   plot(f36(x), x = -1..1,y = -1..1);

end use;

 

does not give me x-points for x < 0.

 

Why?


Alla

 

 

Two comments on RealDomain:

1) I gather from the Help files that Real Domain is geared to precalculus math, so the commands available for it are limited.  That environment, then, would not be suitable for much of calculus, right?

2) What's the most efficient way to switch out of RealDomain?  Exiting the worksheet and re-opening it as well as Restart are options, but they reset a lot of stuff that you might prefer not be reset.  Any other options?

Alla

My original question stemmed from the fact that Maple wouldn't give me any negative x-points in the graph of y= x^(1/3).  It was suggested that I use

 

          plot(Re(x^(1/3)) etc.

 

and this did give me points when x < 0.  But something was still not right since the graph didn't look as I expected.  It was only when I tried Tim's suggestion:

 

         plot(surd(x,3) etc.

 

that the plot came out OK.

 

Alla

 

 

Alec:

I can answer the first question I posed: by factoring & canceling x-sqrt(2) the discontinuity is removed. It is not necessary in this case to assign a value.

As to question 4, I was looking for an actual plot somewhere, but what you posted was Maple code for the graph, not the graph itself.

I'm still left with the issue of whether the "removable discontinuity" belongs in the same typology as the other three discontinuities.

Allan

Alec:

 

Thanks for your patience.  I'm following you up to a point.  If you factor the numerator, you do get x + sqrt(2).  And if you substitute sqrt(2) for x, you get 2*sqrt(2) for the limit.  My questions are:

 

1) Since the limit is found in the same way as any continuous function, why is this called a removable discontinuity?  I thought that meant that some operation (a definition) was necessary to remove the discontinuity, but apparently it means: ignore the discontinuity.  Is that a fair statement?

 

2)  There are three other discontinuities listed in Thomas & Finney.  Two of them -- jump discontinuity (y = x*floor(x) @2) ) and infinite discontinuity (y = 1/(x - 2) @ 2) -- do show up as "undefined" when I ask Maple for the limit.  The third, oscillating discontinuity (y = sin(1/x) @ 0) yields a range of  -1..1, which I understand from Help that this is how Maple responds to that sort of discontinuity.  But we do get a limit in the present case, so is it properly labeled as a discontinuity?

 

3) If Maple had not missed the value x = sqrt(2), would it have drawn the graph differently?

 

4) Could you indicate exactly how I find the correct plot you posted?

 

Again, many thanks for this valuable information.

 

 

 

 

 

 

 

Alla

 

 

Alec:

We are still not communicating too well.  I agree there's a discontinuity at sqrt(2), but why is Maple giving me a limit of 2*sqrt(2) instead of "undefined." And why does plotting show no discontinuity?

Alla

Alec:

Trying x = sqrt(2) yields a limit of 2 sqrt(2).  Still no discontinuity.

Alla

Alec:

Are you saying that the book's error is typographical?  That the discontinuity is at x= sqrt(2), not 2?

Alla

My thanks to djc for the routine, which worked fine.

Two questions:

1) I notice RealDomain was not invoked in the routine.  I assume this is because it is loaded automatically when a worksheet is begun.  Correct?

2) Is it possible to call RealDomain generally so that for a given worksheet the real number environment would replace the complex number environment for every command?

AB

Alec:

Your answer was not helpful.  Let me put it this way: What command can I issue to Maple that will give me the results I specified in my previous entry?

Alla

Remember, I'm talking about putting the standard plus-or-minus symbol into "standard math in a text region."  Again, the pending example is the quadratic formula.  If it is possible to do this, let me see it.

Alla

Thanks for your suggestion, Axel, but how do you use it?  The pending example is the quadratic formula.  Would you please write it out?

Alla

I copied & pasted your quadratic formula, but it doesn't work.   Maple simply replaced

    *\xB1

with

    xB1

Alla

 

I find it weird that

    y = \xB1 x

works, but

   y = \xB1 6

gives a syntax error.

Also, exiting standard math & then adding the 6 doesn't work if you have a complicated expression where +/ is in the middle of the expression,all of which you wish to convert to standard math.  Try, for example, writing the quadratic formula in standard math in a text region.  I hope you can do it.

\xB1 doesn't work.  I tried

           y = \xB1 6

but Maple is unable to convert that to an expression.

Again, I'm inserting  nonexecutable standard math in a text region, using the classic interface in 9.5.

Alla

 

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