As a reference for the calculus part of our course, we are using the excellent book 'Calculus Lifesaver' from Adrian Banner. This book is accompanied by extremely useful free downloadable video lectures with very clear explanations. Sometimes, it is not as deep as we would like it to be, but there is plenty of sources to remedy that when it happens.
In section 5.2.11, one proof of 'Differentiability implies continuity' is laid down, There is a step (step 4) in the proof that involves using a not so obvious trick.
I wanted to try to prove it myself in a more straightforward manner.
Here is what I came up with: http://jadnohra.net/release/math/diff_implies_cont.pdf.
I will let Tom review it and tell me what he thinks, hopefully it convinces him :)