Question

for what values of k is lim x---> infinity sinhkx/cosh2x finite

Answer 1

use the defintion of sinh and cosh:
\[\sinh(x) = {1/2} (e^{x}-e^{-x})\]
\[\cosh(x) = {1/2} (e^{x}+e^{-x})\]
\[\lim_{x \rightarrow \infty} (e^{kx}-e^{-kx})/(e^{2x}+e^{-2x})\]

Answer 2

is that the final answer