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RE: Plot[f[x], {x,a,b}] Not Reaching End Points
*To*: mathgroup at smc.vnet.net
*Subject*: [mg29093] RE: [mg29028] Plot[f[x], {x,a,b}] Not Reaching End Points
*From*: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.de>
*Date*: Tue, 29 May 2001 02:57:21 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
> -----Original Message-----
> From: aes [mailto:siegman at stanford.edu]
To: mathgroup at smc.vnet.net
> Sent: Friday, May 25, 2001 7:48 AM
> To: mathgroup at smc.vnet.net
> Subject: [mg29093] [mg29028] Plot[f[x], {x,a,b}] Not Reaching End Points
>
>
> When I execute
>
> n=0.1; Plot[ (1-x)^n, {x,0,1} ]
>
> the plot stops well short of dropping all the way to the
> baseline on the
> steeply falling edge as x approaches 1 --- even if I use
> PlotRange->All
> or expand to something unreasonable like PlotPoints->10000.
>
> I understand that a Plot routine can have difficulties dealing with
> singularities or rapidly varying functions within the range to be
> plotted -- but it seems surprising to me that it should totally pass
> over or omit an explicitly stated, nonsingular end point.
>
Well, I don't think this to be a bug, but well intended behaviour, which I
consider to be quite useful mostly (i.e. giving the least irritation for all
use cases).
Your example overstresses the plot point sampling algorithm. So if you do
have a very steep function behaviour for an elsewhere flat function graph,
you are free to increase the number of plot points *locally* !
For your case try:
Plot[(1 - x)^n, {x, 1 - 10^#, 1}, DisplayFunction -> Identity] & /@
Range[0, -20, -7];
Show[%, DisplayFunction -> $DisplayFunction, PlotRange -> All]
-- Hartmut
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