Chapter 3.7, Problem 48E

A metal cable has radius r and is covered by insulation so that the distance from the center of the cable to the exterior of the insulation is R. The velocity v of an electrical impulse in the cable is

$v=-c{\left(\frac{r}{R}\right)}^2\ln \left(\frac{r}{R}\right)$

where c is a positive constant. Find the following limits and interpret your answers.

(a) $\underset{R\to r^{+}}{\lim }v$

(b) $\underset{r\to 0^{+}}{\lim }v$