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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.)

 Jun 25, 2016
 #1
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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.

 Jun 25, 2016

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