5. (Review) The hyperbolic cosine and sine functions are defined by sinh(x) = e - ex and cosh(x) = 2 2 (a) Compute the derivatives and antiderivatives of cosh and sinh. (b) Let C be the space curve with parametric equation r(t) = (cosh(t), sinh(t) ) for t E R. Show that C is the right branch of the hyperbola with equation x2 - y2 = 1. (c) The cosh function can be used to describe the curve a rope, - - 60 y = 47.05 cable, or chain hanging between two poles assumes; such a curve is called a catenary. Suppose a hanging cable is parameterized by r(x) = (x, 20 cosh (x /20)) y = 20 for x E [-30, 30], where all distances are in meters. De- x = 0 termine the length of the cable