1. (60 pts.) Using the definitions of the hyperbolic functions cosh(x)=21(ex+ex)sinh(x)=21(exex), the basic properties of Laplace transforms, and tables 3.1 and 2.3, find the Laplace transforms, F(s)=L{f(t)}, of the following functions without explicit integration in the time domain: (a) f(t)=sinh(t) (b) f(t)=cosh(t) (c) f(t)=ebtsinh(t) (d) f(t)=ebtcosh(t) (e) f(t)=tsinh(t) (f) f(t)=tcosh(t)