im considering the boundary of the set
B={z:im(z)<=0 and 2<=z<3} in the complex plane
is the the function
f(z)=1/(sinh(z+2)) bounded on the boundary of B?
im saying no,as the point z=-2 is on the boundary so f is not continuous on the boundary of B
in particular 1/f(z) tends to 0 as z tends to -2 so f(z) tends to infinity.
is this enough to show its not bounded ?
is there a way to show |f(x)|>M for any M directly from f(z)?
thanks