In the case of the Taylor expansion, you can test if the student has correctly memorised the formula and can plug and chug, which is what a lot of my closed book tests were like. But these tests were easy because all I had to do was memorise a few basic formulas.

You can also ask a student to actually explain the motivation for it, as well as its significance. My university exams were all in the form of explaining a few assigned topics to a teacher after being given some time to prepare notes and remember things, without access to prior notes and textbooks. Being able to use notes without restrictions would trivialise that.
Rote memorisation would not work in the case of the exams that I took.