First, f(x) is not defined when x=0. If the function is continuous at this point, then the limit of the function at this point should be equal to the defined function value.

When x tends to 0, cotx~ 1/tanx~ 1/x (equivalent infinitesimal relation)

Then f (x) = (1 -x) (1/x), and if -x is t, then f (t) = (1+t) (- 1/t).

Because the important limit (1+t) (1/t) is equal to e when t tends to 0, f is equal to 1/e when t tends to 0.

Then when x tends to 0, f(x) tends to1/e.