For what intervals is f(x) = tan((pix)/4) continuous?

1 Answer
Nov 13, 2015

tan((pix)/4) is continuous on intervals of the form
(2 + 4k, 2 + 4(k+1)), k in ZZ

Explanation:

tan(x) is continuous on
(pi/2 + kpi, pi/2 + (k+1)pi), k in ZZ

So tan((pix)/4) is continuous where (pix)/4 lies within such an interval. That is, where

pi/2 + kpi < (pix)/4 < pi/2 + (k+1)pi

Multiplying through by 4/pi gives us

2 + 4k < x < 2 + 4(k+1)

Thus tan((pix)/4) is continuous on
(2 + 4k, 2 + 4(k+1)), k in ZZ