A complicated limit involving floor function Let $f(x) = \lfloor x\lfloor1/x\rfloor \rfloor $ . Find $\lim_{x \to 0^{+} } f(x)  $ and $\lim_{x \to 0^{-} } f(x)$ . I think $\lim_{x \to 0^{+} } f(x)$ doesn't exist but I have no idea about $\lim_{x \to 0^{-} } f(x)$ . 

Check the following graph:
You will get the answer automatically.
https://www.desmos.com/calculator/8p190y7wr2
Hint: The limit as a whole is not defined, because negative limit is not equal to positive limit.
