Question: How does the transformation of a region affect its boundaries?

[the1ceman]

Hello. I am trying to work out what the region

\{0\leq\tau\leq t,0\leq t<\infty\} Is under the transformation:

t=u+v,\tau=v

I know its just
\{0\leq u<\infty,0\leq v<\infty\}
But i am having difficulty showing this.
Thanks.

 

[the1ceman]

Anyone?

 

[Defennder]

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

Subtracting v from from the above inequalities give: 0 \leq u < \infty
From the first inequality you should be able to see that 0\leq v<\infty holds.