1. The rate of transmission in a telegraph cable is observed to be proportional to x^2\ln (1/x), where x is the ratio of the radius of the core to the thickness of the insulation ( 0<x<1 ). What value of x gives the maximum rate of transmission?

I overlooked this simplicity of this problem. I just needed to find the deriv of the problem where it = 0. This was .60653019.

2. f(x)=ln(x)/(1+ln(x)^2). Find lim as x->0+ and x-> inf

nevermind, it's 0 for both limits