Unbounded and continuous almost everywhere

[Ja4Coltrane]

Can anyone give me an example of a function f:[a,b]->R which is continuous almost everywhere yet unbounded?

Thanks!

 

[yyat]

The function f:[0,1]->R given by
f(x) = n if x=1/n for some positive integer n
f(x) = 0 else

 

[Ja4Coltrane]

muchas gracias

 

[Ja4Coltrane]

Okay how about one which isn't Riemann (improper) integrable

 

[rochfor1]

$$\displaystyle\sum_{ k = 1 }^\infty k \chi_{ [ 0, \frac{ 1 }{ k^2 } ] }$$

 

[matt grime]

Um, surely f(x)=1/x for x>0 and f(0)=0 is far simpler, and does everything needed.