RE: Plot[(1 + 10^(-k))^(10^k), {k, 2, 9}]

*To*: mathgroup at smc.vnet.net*Subject*: [mg27469] RE: [mg27427] Plot[(1 + 10^(-k))^(10^k), {k, 2, 9}]*From*: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.de>*Date*: Tue, 27 Feb 2001 00:37:21 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

for my answer see below -----Original Message----- From: Hu Zhe [mailto:huzhe at public3.sta.net.cn] To: mathgroup at smc.vnet.net Subject: [mg27469] [mg27427] Plot[(1 + 10^(-k))^(10^k), {k, 2, 9}] Hi, I happen to execute: Plot[(1+10^(-k)^(10^k), {k, 2, 9}] It looks fine if you change {k, 2, 9} to {k, 2, 3}, but otherwise the plot is absurd. Since Limit[(1+10^(-k)^(10^k), k->Infinity]==E may I ask what's wrong with my Mathematica 4.0 on MMX 166 ? Sincerely, Hu Zhe ------------------- The "absurd" data are the result of missing precision. Although you specified your expression to be plotted exacly, Plot will insert machine precision values for the argument k. compare: In[8]:= f[k_] := (1 + 10^(-k))^(10^k) In[9]:= Plot[f[k_], {k, 8., 8.1}] This is a narrow window on the erratic function values plotted In[10]:= ListPlot[Table[f[k], {k, 8., 8.1, 0.001}], PlotJoined -> True] This also happens with Table values (of machine precision), but not so with increased precision: In[11]:= ListPlot[Table[f[k], {k, 8.`16, 8.1`16, 0.001`16}], PlotJoined -> True] Now considering the plot you (presumably) got: In[12]:= Plot[f[k], {k, 2, 9}] After having taking into account for the automatic plot range adaption this may be compared to In[14]:= ListPlot[Table[{k, f[k]}, {k, 6.5, 9, 0.01}], PlotJoined -> True, PlotRange->{{5.5,9},Automatic}] Now, if you specify a precision of at least 5 decimals, this graph will look quite more pleasing: In[15]:= ListPlot[Table[{k, f[k]}, {k, 6.5`5, 9, 0.01`5}], PlotJoined -> True, PlotRange->{{5.5,9},Automatic}] A perhaps better method, that keeps arbitrary precision within Plot is from Ted Ersek (I hope, I remember right), you might like to search at Wolfram's MathSource. (This is Ted's home page: Download Mathematica tips, tricks from http://www.verbeia.com/mathematica/tips/Tricks.html) -- Hartmut Wolf