I'm starting to work with single-supply op-amps for low voltage applications, and have the following, non-inverting setup:
The circuit behaves well with both op amps so long as the predicted output voltage is below ~2.5 V:
I settled on these two op amps because they are affordable, work with V < 5 V, are single supply and, at least in the case of the MCP601, are rail-to-rail. It's clear, however, that there is something funky going on as we approach the positive rail. If I switch R1 and R2 in my circuit, the op-amps behave as predicted, although I don't think this is surprising since the maximum predicted voltage under these conditions is 1.86 V.
I'm still not certain if my application requires a full 3 V range (my intention is to replace the variable resistor with a photoresistor) but I am curious if (a) is it obvious that this circuit should not behave ideally close to the positive rail and (b) what, if anything, in the datasheet warns me of this behavior?