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Plotting w/o artifacts at discontinuities



I would like to be able to get plots that do not have artifacts from
discontinuities without having to know where the problem[s] will be in
advance. 

For example, I would like to be able to say
	Plot[1/(1+x), {x,-2,1}]
and get a graph without the vertical line at x==-1.  Though 
	p1=Plot[1/(1+x), {x,-2,-1}, DisplayFunction->Identity];
	p2=Plot[1/(1+x), {x,-1,1}, DisplayFunction->Identity];
	Show[p1,p2, DisplayFunction->$DisplayFunction]; does the trick, it
requires my anticipation of the problem at x==1.


Thanks.

-Bruce
        Bruce Cohen                    |  INTERNET: bic@cgl.ucsf.edu
        Lick-Wilmerding High School    |           
bic@lick.pvt.k12.ca.us
        755 Ocean Avenue               |  VOICE:    (415) 333-4021
        San Francisco, CA  94112       |  FAX:      (415) 333-9443 -- 
        Bruce Cohen                    |  INTERNET: bic@cgl.ucsf.edu
        Lick-Wilmerding High School    |           
bic@lick.pvt.k12.ca.us
        755 Ocean Avenue               |  VOICE:    (415) 333-4021
        San Francisco, CA  94112       |  FAX:      (415) 333-9443



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