limit of a hyberbolic function?

Question

how do you find the limit of the function below as x goes to infinity

e^(2x)/ sinh(2x)

Answer 1

For x>0 we have e^(2x)/sinh(2x) = 2*e^(2x)/(e^2x) - e^(-2x)) = 2/(1 - e^(-4x)). Since the denominator goes to 1 as x -> oo, it follows the limit is 2.