1. “Sufficiently large” is an important concept in sequences and series. In essence it means any crazy thing can happen for as long as it wants to happen, so long as there is a finite point after which the sequence or series starts behaving in a controlled/predictable way. A finite number of terms can’t affect […]

I like to present totally cooked-up examples demonstrating the reason for certain hypotheses or limitations in calculus, in the hope that they will help students remember and correctly apply the theorems more easily. Here are a few. Note that the sequence has limit 0 but the function oscillates. This is why you can use convergence […]