Re: Asking PlotRange to take a Dynamic value

• To: mathgroup at smc.vnet.net
• Subject: [mg97999] Re: Asking PlotRange to take a Dynamic value
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Fri, 27 Mar 2009 05:37:41 -0500 (EST)
• References: <gqfl0o\$kra\$1@smc.vnet.net>

```Hi,

what's wrong with

Manipulate[
Plot[{Log[x], x^0.2, x^0.25, x^0.3}, {x, 0.01, n},
PlotStyle -> {Red, Blue, Blue, Blue},
PlotRange -> {{1, z}, {0, 55}}],
Style["Log[x] vs. \!\(\*SuperscriptBox[\"x\", \"a\"]\) for small \
positive a 0.2, 0.25 & 0.3", 12, Bold],
{{z, 10, "x from 1 to "}, {10, 500, 10000, 500000}, PopupMenu}, {n,
0.1, Dynamic[z], Appearance -> "Labeled"}]

Regards
Jens

Andrew wrote:
> 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!
>