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Transformation of a region

  1. May 19, 2008 #1
    Hello. I am trying to work out what the region

    [tex]\{0\leq\tau\leq t,0\leq t<\infty\}[/tex] Is under the transformation:

    [tex]t=u+v,\tau=v[/tex]

    I know its just
    [tex]\{0\leq u<\infty,0\leq v<\infty\}[/tex]
    But i am having difficulty showing this.
    Thanks.
     
  2. jcsd
  3. May 22, 2008 #2
    Anyone?
     
  4. May 22, 2008 #3

    Defennder

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    [tex]0 \leq v \leq u+v < \infty[/tex] after substituting u, v for tau and t and combining the inequalities.

    Subtracting v from from the above inequalities give: [tex]0 \leq u < \infty[/tex]
    From the first inequality you should be able to see that [tex]0\leq v<\infty[/tex] holds.
     
    Last edited: May 22, 2008
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