HP Forum Archive 16

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HP50g Graph of 3rd root of x^2 Message #1 Posted by dbatiz on 10 Oct 2006, 9:19 a.m. I hope sombody can shed some light on this for me. Whe I graph Y1(X)=(X^2)^(1/3), I get the correct graph of both positive and negative values of X. But, when I graph Y1(X)=3rd"Radical Symbol"(X^2), I only get the positive side of the equation. I also only get half when I graph Y1(X)=X^(2/3) I've tried changing my CAS settings, and I've not had any luck. Are there special rules for using the "Radical" symbol of the equation writer? Thanks David Batiz

Re: HP50g Graph of 3rd root of x^2 Message #2 Posted by Eric Smith on 10 Oct 2006, 7:21 p.m., in response to message #1 by dbatiz AFAIK the radical symbol (√) generally represents the positive real root. In other words, radical 4 is 2, not -2. If you want +/-2, you use +/- radical 4, or 2^(1/2).

Re: HP50g Graph of 3rd root of x^2 Message #3 Posted by dbatiz on 10 Oct 2006, 11:43 p.m., in response to message #2 by Eric Smith Here’s a subtle difference. If I take the third root of x, then square it, the graph works. But if I square x, then take the cube root, I only get half the graph. I think both processes should produce the same result. Is there anywhere I can read up on this to figure it out? Thanks, David

Re: HP50g Graph of 3rd root of x^2 Message #4 Posted by Marcus von Cube, Germany on 11 Oct 2006, 6:27 a.m., in response to message #3 by dbatiz David, I found a hint in an old HP journal. It is on page 38: Quote: Why do I get a complex number when I evaluate '(-1)^(2/3)' ? The machine returns a complex principal solution for expressions with fractional exponents. To get a real-valued result to the above, use 'XROOT(3,(-1)^2)' ... Complex numbers aren't plotted, of course. If you switch to degrees and polar display, and use ->NUM to force a numeric result, you get (1.,<)120.) for (-1)^(2/3). Other possible solutions include (1.,<)-120.) and (1.,<)0.). Marcus

Re: HP50g Graph of 3rd root of x^2 Message #5 Posted by dbatiz on 11 Oct 2006, 8:07 a.m., in response to message #4 by Marcus von Cube, Germany Marcus, By pressing the edit button twice on my "Y=" screen, I edited my equation to "Y1(X)=XROOT(3,X^2)". I agree this should provide real-value results, but for some reason the calculator refuses to plot the left side of the graph. The XROOT(3,X^2) works for both negative and positive values of X in the stack, but something keeps it from working in the graph. Also, it will not generate solutions in the "TABLE" for negative values of X. It returns "Undef." Thanks for your replies, David

Re: HP50g Graph of 3rd root of x^2 Message #6 Posted by Marcus von Cube, Germany on 11 Oct 2006, 9:13 a.m., in response to message #5 by dbatiz David, Quote: The XROOT(3,X^2) works for both negative and positive values of X in the stack, but something keeps it from working in the graph. That's funny! I've just tried 'XROOT(3,SQ(X))' which works fine. The Exponent symbol "^" seems to cause the trouble. This is probably more of a bug than a feature. Marcus

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