A heavy rope, 40 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 90 ft high. (Let x be the distance in feet below the top of the building. Enter x,* as x;.) (a) How much work W is done in pulling the rope to the top of the building? Show how to approximate the required work by a Riemann sum. lim Ax Express the work as an integral. dx Evaluate the integral. ft-lb (b) How much work W is done in pulling half the rope to the top of the building? How much work W is done in pulling half the rope to the top of the building? Show how to approximate the required work by a Riemann sum. lim 1-+00 AX Express the work as an integral. dx Evaluate the integral. t-lb A heavy rope, 30 ft long, weighs 0.8 lb/ft and hangs over the edge of a building 100 ft high. How much work W is done in pulling the rope to the top of the building? (a) How much work W is done in pulling the rope to the top of the building? Show how to approximate the required work by a Riemann sum, then express the work as an integral and evaluate it. (b) A heavy rope, 30 ft long, weighs 0.8 lb/ft and hangs over the edge of a building 100 ft high. How much work W is done in pulling half the rope to the top of the building? Tutorial Exercise A force of 7 lb is required to hold a spring stretched 3 in. beyond its natural length. How much work W is done in stretching it from its natural length to 6 in. beyond its natural length