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Re: Function research

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105915] Re: [mg105913] Function research
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Fri, 25 Dec 2009 00:34:36 -0500 (EST)
  • Reply-to: hanlonr at cox.net

f[x_] = 1/(x^2 - 1);

excl = x /. Solve[Denominator[f[x]] == 0, x]

{-1,1}

Plot[f[x], {x, -4, 4},
 Exclusions -> Thread[x == excl],
 ExclusionsStyle ->
  Directive[Red, AbsoluteDashing[{10, 10}]],
 PlotStyle -> Directive[Blue, Thick],
 PlotRange -> {-5, 5}]

Maximize[{f[x], Abs[x] < 1}, x]

{-1, {x -> 0}}

Quiet[Minimize[{f[x], #}, x] & /@ {x < -1, x > 1}]

{{0, {x -> -Infinity}}, {0, {x -> Infinity}}}

Limit[f[x], x -> #] & /@ {-Infinity, Infinity}

{0,0}


Bob Hanlon

---- Arnold <sender999ster at gmail.com> wrote: 

=============
How means Mathematica 5.2 it is possible to discover a range of definition of function and a function range?
Example: 1 / (x^2-1).
Thanks.



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