\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Apply Heine's theorem to conclude that \(f(x) = e^x\) is uniformly continuous on every segment \([a, b] \subset \mathbb{R}\), but not uniformly continuous on \(\mathbb{R}\) as a whole.
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.