9. Consider a uniform cable with density 8 hanging in equilibrium. As shown in Figure 1.12, the tension forces T(x + Ax), -T(x), and the weight of the piece of cable lying over [x.x + Ax] all balance. If the bottom of the cable is at x = 0, To is the magnitude of the tension there, and the cable is T(x+Ax)/ +Ax 10+ ΔΕ -T(x) -g8As x+Ax FIGURE 1.12 g8 the graph y= To = f(x), show that ƒ"(x) = √1 + f'(x)². (Remember that tan 0 = f'(x).) Letting C = To/g8, show that f(x) = C cosh(x/C) +c for some constant c. (Hint: To integrate : make the substitution u = sinh v.) du