Is the function $u=2x-3y+5$ uniformly continuous in the infinite plane $\mathbb{R}^2$?
2026-04-03 12:42:05.1775220125
is the function $u=2x-3y+5$ uniformly continuous?
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Let $\vert x-a\vert<\frac{\epsilon}{4}$ and $\vert y-b\vert<\frac{\epsilon}{6}$, then $\vert 2x-3y+5-2a+3b-5\vert\leq 2\vert x-a\vert + 3\vert y-b\vert<2\frac{\epsilon}{4}+3\frac{\epsilon}{6}=\epsilon$.