3 ms·

Thanks! I think you don't even need arctan for this. Just put one of Myhill's "bumps" at x=0 and shrink it down. That function approaches f(x)=0 for all x bu

by lisper 2y ago

Thanks! I think you don't even need arctan for this. Just put one of Myhill's "bumps" at x=0 and shrink it down. That function approaches f(x)=0 for all x but its derivative at x=0 remains 1.

ogogmad 2y ago
The arctan has the advantage that it's differentiable infinitely many times over R.