1. The correspondence L_f=L_i (I+QAT) is a valid approximation when the average expansion coefficient is small. If a is large, you must integrate the relationship dL/dT = a L to determine the final length. A) Assuming that the coefficient of linear expansion is constant as L varies, determine a general expression for the final length. b) Given a bar 1.00 m long and a temperature change of 100.0'C, determine the error caused by the approximation when a = 2.00 x 10-"('C)~+ (a typical value for a metal) and when a= 0.020 0 ( C)~+ (an impractical large value for comparison). 2. A steel wire and a copper wire, each 2,000 mm in diameter, are joined end to end. At 40.0'C, each has an unstretched length of 2,000m. The wires are connected between two fixed supports 4,000m apart on a table. The steel wire extends from x=-2,000m to x=0, the copper wire extends from x=0 to *=2,000m, and the tension is negligible. Then the temperature drops to 20.0'C. At this lower temperature, find the tension in the wire and the x-coordinate of the junction between the wires