What the hell is this equation? Aproaching zero, y became fractalized (?). It goes up and down in incredible way.

so do many other functions. and compared to them this is a pretty nice function

 

limit of y as x tends to 0 does exist

 

as

 

0<= x exp(sin(1/x)) <= ex

0 - > and ex -> 0 as x -> 0

 

there fore by sandwiching y tends to 0 as well

(in case you're wondering, the xe comes from the fact that for any number, [math]-1 \leq \sin(x) \leq 1[/math] so we can use the squeeze rule).