\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f \in C([a, b], \mathbb{R})\). Show that there exists a sequence \((\varphi_n)\) of step functions on \([a, b]\) such that \(\varphi_n \to f\) uniformly AND each \(\varphi_n\) is real-valued \(\ge 0\) if \(f \ge 0\). Hint: preserve sign in the T2.1 construction.
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.