#### Problem 94E

Suppose that the temperature in a long thin rod placed along the x-axis is initially C/(2a) if |x|a and 0 if |x|a. It can be shown that if the heat diffusivity of the rod is k, then the temperature of the rod at the point x at time t is T(x,t)=Ca4kt0ae(xu)2/(4kt)du To find the temperature distribution that results from an initial hot spot concentrated at the origin, we need to compute lima0T(x,t) Use 1Hospitals Rule to find this limit.