HP 50g a few questions - Printable Version +- HP Forums (https://archived.hpcalc.org/museumforum) +-- Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum-1.html) +--- Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum-2.html) +--- Thread: HP 50g a few questions (/thread-136486.html) |
HP 50g a few questions - Jonathan Vogel - 04-25-2008 Ok I have a couple questions about the HP 50g: 1) How can I solve ln(x)=x-2 Even in approx mode when I use "solvex" it returns "error: not reducible to a rational expression." How can I solve this without graphing? It is really a pain to graph with the 50g, so I have to bust out my ti-83 which isn't hard but I'd rather do it all on this calculator.
2) How can I find the area between two curves without setting up an integral? Like I want to find the area bounded by y=5sin(1/2x) and y=3 and y=0 ... But let's just say I was dumb and didn't know how to set up an integral to evaluate this. How can I graph these functions and calculate the area bounded between them? This would be rather useful for some things and to check integrals. Someone told me it was possible on the ti-89 so just wondering.
Re: HP 50g a few questions - Hal Bitton in Boise - 04-26-2008 Hi Jonathan, Re: HP 50g a few questions - Karl Schneider - 04-26-2008 Jonathan --
Quote: The error message, of course, results from algebraic intractability of the simple expression: There is no closed-form symbolic solution, so the answer must be obtained numerically. How to do that is the specific question you should be asking. I do not have an HP-50g, but I do have its predecessor HP-49G, which is almost identically organized. It gives the same error message when symbolic solution is attempted. The HP-49G and HP-50g have a numeric-solution menu "NUM.SLV", which provides an input form for providing an equation and a single numeric guess. The two solutions can be obtained separately as Hal suggested, with appropriate guesses. Not surprisingly, the "inflection point" of the input guess -- the dividing line for which result is provided -- is at or near x = 1, which is the root of the function's derivative. The techniques of max/min calculus show that f(1) = 1.00 is a local maximum.
f(x) = ln(x) - (x-2)
Quote: At first I thought that this was a silly question, but again, your real query is how to obtain the correct result graphically on the HP-50g without a formal symbolic or numeric integration. Hal has provided an approach, but it seems to me like a replacement of fundamental mathematics with a sequence of procedures. The calculated "area" may or may not correspond with the visual area on the screen, because the scale of the axes might be quite different. Moving cursors isn't the best way to exactly specify numerical values, either. Hal stated, "I'm pretty sure it uses the same algorithm as the numerical integrator to do this." Maybe, maybe not. The simplest and quickest way to estimate the area is by basic quadrature -- Riemann sums of "sliver" rectangles -- using the already-calculated data points of the two curves (assuming that those were saved, but there's plenty of RAM for it). However, that's not the numerical-integration algorithm. Setting up an integral using the right-shifted (orange) integration function above "TAN" isn't too hard on the HP-50g:
1 2 '3*X-2' 'X' ENTER (integral) yields the correct result of 2.50 as the integral of f(x) = (3x-2).dx between 1.00 and 2.00. For the area between two curves, just define the integrand as the difference between the two functions, f(x) - g(x). There's also "INTVX" and "RISCH" for integration, underneath the "CALC" menu.
It's more challenging to program a chained process of rootfinding and integration. The following archived thread concerned automated numerical solution as input to integration within a program -- using RPL-based calc's (like the HP-50g) versus using the earlier RPN-based calc's. http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv014.cgi?read=51650#51650 ... and a subsequent follow-up: http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv015.cgi?read=83010#83010 -- KS
Edited: 27 Apr 2008, 4:01 p.m.
Re: HP 50g a few questions - Jonathan Vogel - 04-27-2008 Thanks for the responses. I'll try to address each of your thoughts: 'Just out of curiousity, what makes a TI-83 (supposedly) so much easier to plot with'
Hal, I attempted to use your method to find area between two curves and got the wrong answer multiple times. Try to do your method and compare it to the actually answer because I would get like .97 and the actual answer would be 1.93.
Also Karl, I asked to find the area between two curves using the graphing utility to check my answers. I know how to do it using calculus (integrating) and I am pretty darn familiar with the standard integrating capabilities of the calculator but thanks for mentioning that. Now let me ask something else based on your last two links you sent me. Is there a 50g program that will calculate the area between two curves based on the equations in stack 1 and 2?
Thanks.
Re: HP 50g a few questions - bt_schmidt - 04-27-2008 Quote: uh oh. ...bt
PS. Don't you hate it when people quote out of context? <gr>
Re: HP 50g a few questions - Jonathan Vogel - 04-27-2008 Quote:
Huh?
A few things, Jonathan... (HP 50g a few questions) - Karl Schneider - 04-27-2008 This Forum is primarily intended as a place for discussion, not as a "quick free help" message board. (Have you tried comp.sys.hp48?) From the tell-tale careless and conversational manner in which you have phrased your questions and stated your replies, I would assume that you are a high-school student or college undergrad. Most of us here are middle-aged technical professionals. Two of us have graciously addressed your questions; I'm really not quite sure how to characterize your response --
Quote: No one owes you any assistance, so you ought to be more courteous in your requests. Here's another link, which contains some pearls of wisdom: How to Ask Questions the Smart Way
Quote: Until I read between the lines, the basic response that came to mind was along the lines of, "Hypothetically speaking, you should RTFM, and learn how to do it. This is fundamental mathematics."
Quote: Are you sure that you stated this correctly? What are the limits of x? Are you interested in the positive values of the function that are less than 3? Did you really mean "(1/2x)" -- which becomes (positive or negative) infinite as x approaches zero, and can make for a nasty integral that would be difficult to estimate by graphical methods? Or did you mean "(x/2)"? How exactly should Hal (or I or anyone else, for that matter) obtain your "actual" answer? The bottom line is, you really ought to invest more in thought, effort, and time to proofread before posting questions that will require time and effort from others to answer.
As you might have gathered from the two archived links of 2004, I'm neither an expert about, nor an enthusiast of RPL-based (HP-28/48/49/50) calc's. I also find them difficult to use. I prefer the old, classic RPN-based models (e.g., HP-15C/42S/32SII). Now, as for your other questions: 1. How can I solve ln(x)=x-2 I'm having the same difficulties on the HP-49G. "SOLVE" or "SOLVEVX" are designed to find symbolic solutions, for which none exist in this problem. Setting flags -03 (numerical result) and -105 (approximate mode) only seemed to force their changing to the appropriate settings for symbolic solutions. These functions can find roots for polynomials, even when the symbolic solutions would be quite complicated (e.g., cubic and quartic). The key here might be "rational", as any polynomial can be factored into linear and quadratic terms (although the quadratic terms might not have any real-valued roots). A numeric-solution stack-based alternative to "NUM.SLV" is "ROOT"
'LN(X)=X-2' 'X' 0.5 ROOT yield the two answers. If "SOLVEVX" fails, you can put 'X' and a random "guess" value onto the stack, and you will likely get a numeric answer. (Curiously, "ROOT" is missing from the HP-49G manual, although both the HP-48G and HP-49G have it.) The "guess" is used to direct the rootfinder toward the value you seek. There might be other roots that you don't want, or local minima/maxima that may foil the solver. If there is only one root in a monotonic function, the solver will find it, no matter what guess is provided. Rest assured that the solver algorithm (TI's or HP's) will use some guess to start the process...
Quote: If you understand what's going on in the RPL program listed in my second link, that's a good template for a simpler one that will accomplish that. There are RPL experts here who could surely spoon-feed to you what you seek, but that's strictly their prerogative to do so... -- KS
Edited: 28 Apr 2008, 2:44 a.m.
Re: HP 50g a few questions - Walter B - 04-28-2008 Quote:Jonathan, are you sure you want to think when reading? d;) Re: HP 50g a few questions - Hal Bitton in Boise - 04-28-2008 Hi again Jonathan, Re: A few things, Jonathan... (HP 50g a few questions) - Jonathan Vogel - 04-28-2008 I'm sorry I acted so rude. Honestly, there are no other forums that discuss HP calculators so this was basically my only choice. I also wasn't aware that this forum was for discussion only. As well... the user base for the 50g is so small that I can barely find ANYTHING when I research its features. I usually just stick with the 800 page manual. Since you guess don't enjoy me bothering you over petty things, can you guys suggest a place where I can ask questions like this?
Again I apologize that I came off rude.
Re: A few things, Jonathan... (HP 50g a few questions) - George Bailey (Bedford Falls) - 04-29-2008 Quote:
This IS the right place for questions like yours. And you already worked on that rude thing, didn't you? ;-)
Cheers, Re: A few things, Jonathan... (HP 50g a few questions) - Karl Schneider - 04-29-2008 Jonathan -- I never said that you were "rude". (There have been only a few genuinely and chronically rude visitors over the years -- part of the reason an account is required for posting.) I did suggest that you be more considerate in posting queries by formulating them more precisely, stating them clearly and completely, and proofreading them carefully. Judging from content in your last two posts, I believe that you can do that. It can be rather annoying, after having made the effort to provide an informative and responsive answer to the questions as they were stated, then be told in so many words, "Thanks, but I already knew that", or, "I'd rather not do that." It represents a considerable shift of burden from the questioner to the respondents. While the primary intent of the Forum is discussion, "how to" questions -- particularly for difficult or unusual tasks -- are certainly not out of line. Accepted etiquette as described in the "How To Ask Questions" link should apply. I would have phrased your two original questions this way:
2. How can I estimate the area between two curves using the sets of plot data, instead of integration? On the subthread ending in "Jonathan, are you sure you want to think when reading? d;)": We technical professionals do expect people to think when using their calculators, rather than to blindly accept whatever output is provided. Providing a starting point (or "guess") for numerical rootsolving is not only reasonable, it's good practice for the reasons I stated. The TI-82 allows the user to provide one or two guesses for SOLVE, as does the HP-50g. Trust me, nothing is "petty" with the RPL-based models. RPL can make difficult tasks easy, but they tend to make easy tasks difficult. I have no intent of becoming truly proficient with my three RPL-based calc's. I bought them for their capabilities, but I've learned only enough about them to get by. The TI models are designed for scholastic use; I also find them more straightforward. Your tip on graphing with the TI-83 was helpful, and I applied it successfully on my used TI-82.
Quote: The best place for run-of-the-mill "how-to" questions regarding the HP-48 and its successors is the newsgroup comp.sys.hp48, as I had previously stated. It gets a lot of traffic, so some searching will be necessary. Best regards, -- Karl S.
Edited: 29 Apr 2008, 1:01 a.m.
Re: A few things, Jonathan... (HP 50g a few questions) - James M. Prange (Michigan) - 04-29-2008 For all RPL models, the comp.sys.hp48 usenet group is probably the best place to search for answers or ask questions. If you have a news client installed, you may be able to access it through an NNTP server, or you can access it through your web browser at http://groups.google.com/group/comp.sys.hp48/. I recommend that you search for an answer in that Google archive (all the way back to 1991), and then, if you don't find it, ask on the newsgroup. Another excellent place to find information, programs, and libraries for RPL models is http://www.hpcalc.org/.
Regards, Re: A few things, Jonathan... (HP 50g a few questions) - Giancarlo (Italy) - 04-29-2008 Hi Jonathan. |