Piecewise smooth functions

[jaejoon89]

I'm trying to find a Fourier series for exp(-ax) where a is a positive constant. How is exp(-ax) piecewise smooth?

 

[CompuChip]

It is piecewise smooth in one big piece

If you take piecewise smooth to mean: smooth in all but finitely many points, it satisfies the definition because the number of points in which it is not smooth is zero ($< \infty$).