For what values of k is lim x -> INF coshkx/sin2x finite?

Answer 1

For any non-zero value of k, cosh(kx)->∞ as x->∞

For k=0, cosh(kx)->1 as x->∞

However, the numerator being finite does not make the limit existent because the denominator is undefined as x->∞ because sin(2x) as x->∞ is undefined. (It oscillates).

Answer 2

For what values of k is lim as x approaches infinity of (coshkx)/(sinh3x) finite?

Enter your answer as an interval or list of intervals, for example, (-infinity,3], (5,7).