Asking PlotRange to take a Dynamic value

*To*: mathgroup at smc.vnet.net*Subject*: [mg97951] Asking PlotRange to take a Dynamic value*From*: Andrew <dr.a.graham at googlemail.com>*Date*: Thu, 26 Mar 2009 05:23:20 -0500 (EST)

Hello, I apologise in advance for what is probably a stupid question, but I would appreciate some help in persuading PlotRange to take a Dynamic value - or suggesting another way to go about things entirely! For teaching purposes I wanted to draw a series of graphs of Log[x] vs. x^a for small positive values of a at different scales (simply to illustrate how Log[x] is eventually < x^a, for any positive a). I thought I would use Manipulate to allow students to explore this interactively. E.g for x=0 to 10: Manipulate[ Plot[{Log[x], x^0.2, x^0.25, x^0.3}, {x, 0.001, n}, PlotStyle -> {Red, Blue, Blue, Blue}, PlotRange -> {{0, 10}, {0, 3}}], Style["Log[x] vs. \!\(\*SuperscriptBox[\"x\", \"a\"]\) for small \ positive a 0.2, 0.25 & 0.3", 12, Bold], Style["x = 0 to 10", 12, Bold], {n, 0.01, 10, Appearance -> "Labeled"}] & for x=0 to 500,000: Manipulate[ Plot[{Log[x], x^0.2, x^0.25, x^0.3}, {x, 0.001, n}, PlotStyle -> {Red, Blue, Blue, Blue}, PlotRange -> {{0, 500000}, {0, 55}}], Style["Log[x] vs. \!\(\*SuperscriptBox[\"x\", \"a\"]\) for small \ positive a 0.2, 0.25 & 0.3", 12, Bold], Style["x = 0 to 500,000", 12, Bold], {n, 0.01, 500000, Appearance -> "Labeled"}] But rather than a series of separate graphs I thought it would be more elegant to combine them in one plot with a Dynamic value to choose the scale, e.g.: Manipulate[ Plot[{Log[x], x^0.2, x^0.25, x^0.3}, {x, 0.01, n}, PlotStyle -> {Red, Blue, Blue, Blue}, PlotRange -> {{1, Dynamic[z]}, {0, 55}}], Style["Log[x] vs. \!\(\*SuperscriptBox[\"x\", \"a\"]\) for small \ positive a 0.2, 0.25 & 0.3", 12, Bold], Row[{Style["x", Bold], " from 1 to ", PopupMenu[Dynamic[z], {10, 500, 10000, 500000}]}], {n, 0.1, Dynamic[z], Appearance -> "Labeled"}] Unfortunately, although the graphs will plot, with continually updating axes, what I really want is to change the plot range for each value of x & fix it so one can see the curves evolving more easily. I hope the 2 individual examples above make it clear what I hoped for - essentially, to click from one to the next with the PopupMenu. The error message reads (e.g. for x=10): Plot::prng: Value of option PlotRange -> {{1,10},{0,55}} is not All, Full, Automatic, a positive machine number, or an appropriate list of range specifications. >> What's gone wrong? PlotRange -> {{1,10},{0,55}} looks like "an appropriate list of range specifications" to me! Any advice appreciated Best regards Andrew Graham