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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