Keep in mind lots of high school math teachers are just bad at their job when it comes to calculus.
I do recall when first taking calc they briefly mentioned delta-epsilion proofs and limits but really hand waved past it, which i guess would be hard if you want everything on solid foundations.
8th Grade or so in Germany, my son got a tricky system of linear equations to solve. I showed him how to solve it in Python and also explained him how to quickly go back to fractional notation instead of floats (0.133333... = 2/15).
As the teacher looked at the results, he said I should receive a Nobel for my work. As my son told me that, I had a very long sigh...
I don't think you deserve a Nobel, but I do think that teaching your son to solve lots of different problems with algorithmic recursion is going to help him much more in life than memorizing the way to solve one problem on a math test.
I don't think I ever understood math except where it was logical, within the bounds of what I could deduce. But when I learned to write recursive algorithms, that capacity for deduction expanded exponentially.
I do recall when first taking calc they briefly mentioned delta-epsilion proofs and limits but really hand waved past it, which i guess would be hard if you want everything on solid foundations.