I created these images with an external tool.
The first image below is intended to represent the definition of limit, $ \lim_{x \to c} f(x)=L$, using the epsilon-delta $(\epsilon-\delta)$ and show that, in the rectangle of sides $]c-\delta, c+\delta[\times ]L-\epsilon,L+\epsilon[$, the behavior of $f(x)$ can be any (the curves depicted in violet color).
The following image tries to explain to my 18-year-old students the concept of vertical and horizontal asymptotes of a real function of real variable,
drawing only some nearby tracts of functions and their asymptotic curves. I looked at a lot of English textbooks: precisely
- Calculus 8th J. Stewart;
- Calculus Adams 9ed 2018;
- Calculus Larson-Edwards 10ed 2014;
- Calculus ROBERT T. SMITH AND B. MINTON;
- PreCalculus Ron Larson and other in Italian language.
but I do not remember where I have seen these drawings. I'd thank anyone who could find an exact reference. Thank you for everything.