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# [HP Prime] Euler Constant infinite limit definition

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HP Prime Graphing Calculator

Has someone tried to obtain the Euler Constant by its infinite limit definition?

Maybe this bug hasn't been reported yet. I suggest it to be fixed by the release of next FW public update.

Thenk you.

Regards,

Ciro.

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Hello Ciro,

please try this one:   lim ((1+1/x)^x), the only change a pair of extra brackets. I have no prime, but maybe this is the reason for failure...

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Hello CalcPeace

It has worked the way you suggested.

Then I understand that the exponent X works like power for the whole limit operand, as if it has been envolved by an extra bracket with X power outside. In fact, trying other argument, it answers the limit result powered by X, regardless this X and the one inside limit brackets are the same.

Being so, "lim" (limit operand) preceeds power operand.

Then I guess it should be mentioned in manual, on page 26, under "Algebraic precedence". I haven't thought about this matter before ans I was thinking that it should be typed just like we're currently used to do.

Searching for Euler Constant in the internet, I found it in Wikipedia (https://en.wikipedia.org/wiki/E_(mathematical_constant)) just like this:

I came directly from HP 41cx to HP Prime recently and been led to understand that the calculator's world is able to read expressions as we see them in the books, obviously under certain restrictions. So, these restrictions must be very clear.

That's why I think it would be important this one to be mentioned in manual. That's the suggestion I leave here for the Developers.

Thank you very much.

Best regards,

Ciro.

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I disagree this needs mentioning or is a bug. It is behaving exacty constently and correctly following normal behavior of any 2D equation editor I've ever seen. How could it just "know" that you mean to enclose two objects with one power function? How about this case?

abs(1+2+3+4+5|). <--- cursor is at the | location and when you press ^ what should happen? Should it do a power on all the 1+2+3+4+5? Or only the 5?

What could be improved for certain is the ability to more easily select previous expressions and thus make it easier to apply the power. Also, this may be a case where it shouldn't strip the display of the parenthesis. That second one is debateable however.

TW

Although I work for the HP calculator group as a head developer of the HP Prime, the views and opinions I post here are my own.
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The limit operator is unbreakingly connected with a pair of parentheses, and it acts on the content between the parentheses, and not on anything outside them.

The limit operator does not differ in this sense from any function.

For instance, SIN is always used in the form SIN(….), where SIN acts on the content between the parentheses.

So SIN(x^2) takes the sin of x^2, and SIN(x)^2 takes the sin of x.

When you tap the templates key, and select the limit symbol, in the command line you see these parentheses, and it is indicated that the argument should be within them.

In cases of doubt you can always switch to algebraic view, in Home settings.

You can set the input to algebraic view on page 1, and the history to algebraic view on page 2.

A description of the algebraic form of the limit operator is given on page 367 of the user guide.

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Hi!, @Ciro_Bruno:

You can see too, with Wolfram Alpha, the result's ...

Kind Regards !.
Have a nice day !.
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/
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@Tim_Wessman wrote:

I disagree this needs mentioning or is a bug. It is behaving exacty constently and correctly following normal behavior of any 2D equation editor I've ever seen. How could it just "know" that you mean to enclose two objects with one power function? How about this case?

abs(1+2+3+4+5|). <--- cursor is at the | location and when you press ^ what should happen? Should it do a power on all the 1+2+3+4+5? Or only the 5?

What could be improved for certain is the ability to more easily select previous expressions and thus make it easier to apply the power. Also, this may be a case where it shouldn't strip the display of the parenthesis. That second one is debateable however.

Hi Tim,

I thought the Prime was a scientific calculator in which operator precedence used - i.e. putting a ^ where the cursor is would only operate on the 5. Or is this now a financial calculator where chain calculation is used?

-Bart
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@Ciro_Bruno wrote:

.....(edited for brevity)

That's why I think it would be important this one to be mentioned in manual. That's the suggestion I leave here for the Developers.

Thank you very much.

Best regards,

Ciro.

Hi Ciro,

Although it would be more complete for the manual to include function call in its list of precedence, it is already accepted that a function call takes precedence over a power (this is what Jan_D explained).

Thus

Lim(1+1/x)^x

the function Lim with the argument in paranthesis gets evaluated before the power and we should know to write

Lim((1+1/x)^x) if we wish to include the power as part of the argument of the Lim function.

Best regards.

-Bart
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That's exactly what I had in mind.

In algebraic mode, I wouldn't dismiss the parenthesis. But in textbook mode, I'd write it the way I'm used to read in textbooks. After all, I understood that the term "textbook" ment we could type exactly the way we read in text books. And it seems that WolframAlpha agrees on this idea.

However, HP is free to apply its own meaning for "textbook" entry mode. I don't see any problem on that. I guess the freedom to program functions its own way is the key to break the boundaries for power enhancement.

I see that this is DEFINITELY NOT A BUG, since that's a correct way to write it and obtain the propper result. Still, I can't see what's the problem on mentioning it in manual. As we see in the picture sent by Maké, I'm not the only one who would write it withot parenthesis, WolframAlpha also did it this way. Furthermore, the manual tells about the most basic kinds of precedence order, such as multiplication before addition, meanning I can't see why this so controversial matter shouldn't be there as well.

Pehaps we shoud have in mind that the transition from algebraic entry mode to textbook is a bit more tricky than it looks like. Possibly that's the reason why algebraic came first and we're still spending some time on discussing textbook. I guess the reasoning of "is implicit" isn't the best approach for such gray zones.

Thank you all.

Regards,

Ciro.

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