Transformation of a region

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  • #1
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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.
 

Answers and Replies

  • #2
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Anyone?
 
  • #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.
 
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