Question

List the discontinuities for the function f(x) = cot( 2x/3)
a: n(3pi/2) when n is an integer
b: n(pi/2) when n is an integer
c: n(pi/3) when n is an integer
d: there are no discontinuities

Answer 1

\[f(x) = \cot(2x/3) = \frac{ \cos(\frac{ 2x }{ 3 }) }{ \sin (\frac{ 2x }{ 3 }) }\]
the discontinuity happens when sin(2x/3) = 0
if you make x = 3pi/2 you find that sin(2*(3pi/2)/3) = sin(pi) = 0

Answer 2

I found (a) as answer

Answer 3

thanks!