I'm currently working on an assignment where I have to find the supremum of $\{4x-2y:x,y \in \mathbb{R}, x^2+y^2<4\}$. Please don't give me the solution, just some ideas as to how I can work this out.
2026-04-06 15:20:14.1775488814
What is $\mathrm{sup}\{4x-2y:x,y \in \mathbb{R}, x^2+y^2<4\}$?
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Use $s$ the value of the supremum. $4x-2y=s$ is an equation for a line. The point $x,y$ is part of the disk. You get a maximum or minimum value for $s$ when the line is tangent to the disk