Consider the following.
f(x) = tan(πx/2)
Find the x-values at which f is not continuous. Are these discontinuities removable? (Use k as an arbitrary integer. If an answer does not exist, enter DNE.)
The function f(x) = tan( pi·x/2 ) is discontinuous at pi/2 + k·pi for all integer values of k (including negatives).
These discontinuities are NOT removable because the y-value approaches + infinity from the left and - infinity from the right at each of these discontinuities.