For example, the main tool of analysis are basic inequalities like the Cauchy-Schwarz inequality and in a limit proof, you need to know which one to use to produce the right choice of epsilon for every delta. The huge mistake a lot of mathematics programs today make is that they teach students in basic calculus that these 2 types of problems are completely different-that substituting a $u$ in an integral is a completely different and reasonable problem for humans to do and calculating a limit using epsilons and deltas is an alien problem for geniuses. It's crap-the only difference is that in the latter, you can't just mechanically solve the problem, you have to think about it. To me, this is one of the hidden reasons students struggle with analysis even though they did great in baby calculus-they're conditioned to think it's something only geniuses can do. It is more difficult than the calculus they're used to, but it's not a different procedure-it's the same in kind. It just needs to be understood better before proceeding.