Find the points of discontinuity of the function
if they exist.
The function exists for all x
, however it is defined by two different functions and, therefore, is not elementary.
We investigate "behavior" of the function near to the point x = 0
where its analytic expression changes.
Calculate one-sided limits at x = 0
Thus, the function has a discontinuity of the first kind at x = 0
The finite jump at this point is
The function is continuous for all other x
, because both the functions defined from the left and from the right of the point x = 0
are elementary functions without any discontinuities.