Conversation started May 16, 2023 at 23:07.
Ted Shifrin
Ted Shifrin
May 16, 2023 23:07
@D.C. All right. Here's the summary. I suggest you draw this stuff in the $uv$-plane. You recall that you noted that $x\ge 0$ corresponds to the half-plane $u+v\ge 0$. So you want to be positioned in that half-plane.
D.C. the III
D.C. the III
right
shintuku
shintuku
even $y=0$?
D.C. the III
D.C. the III
I got that bound
Ted Shifrin
Ted Shifrin
$y+x^2=0$ becomes *either* $v=0$ *or* $2u+v=-1$.
$x-y=2$ becomes *either* $u=1$ *or* $u=-2$.
$x^2-2x+4y=0$ becomes *either* $v=u$ *or* $3u+v = -2$.
Your goal is to select a region in $u+v\ge 0$ which maps one-to-one to our region bounded by the three curves.
D.C. the III
D.C. the III
Ok. I'm going to work them out just to see how you reasoned them
Ted Shifrin
Ted Shifrin
May 16, 2023 23:10
I did high-school algebra and factored.
 
Conversation ended May 16, 2023 at 23:10.