I want to show that the piece wise function $f(x)=x$ for $0\le x<1$ Or $f(x)=x^3$ for $1\le x\le 2$is uniformly continuous. I can show uniformly continuous on each interval separately but how do I show uniform continuity on of the whole function on the entire interval.
2026-04-05 20:14:28.1775420068
Uniform continuity of piece wise function
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You do not have to use the definition. Observe that $f$ is continuous map on a compact (or closed and bounded) interval to the real numbers, hence, it must be uniformly continuous. If you are not familiar with this result, you may want to take to a look here.