Consider the following Fx tanpix2 Find the xvalues at which

Consider the following. F(x) = tan(pix/2). Find the x-values at which f is not continuous. Are these discontinues removable? (Use k as an arbitrary integer. If an answer does not exist, enter DNE.) x = pi/2 + pik.

Solution

f(x) = tan(x/2)

tan(x/2) is discontinuous at x/2 = /2 + k

==> x = (2/)( /2 + k)

==> x = 2( 1/2 + k)

==> x = 2(1 + 2k)/2

==> x = 1 + 2k

Hence for x = 1 + 2k , tan(x/2) is discontinuous