How to find the discontinuous point of function, such as f (x) = (x ^ 3-x) / sin π x, find the How to find the discontinuous point of function, such as f (x) = (x ^ 3-x) / sin π x, find the discontinuous point of function

How to find the discontinuous point of function, such as f (x) = (x ^ 3-x) / sin π x, find the How to find the discontinuous point of function, such as f (x) = (x ^ 3-x) / sin π x, find the discontinuous point of function

F (x) = (x ^ 3-x) / sin (π x) = x (x-1) (x + 1) / sin (π x) consider the point of sin (π x) = 0, 1. X = 0, x = - 1, x = 1. The first kind of removable discontinuity ∵ LIM (x - > 0) f (x) = - 1 / π, LIM (x - > - 1) f (x), LIM (x - > 1) f (x) also exist; 2. X = ± 2, ± 3, ± 4 The second kind