I don't know how to prove Exercise 1.x.11 on Page 43 of Brenner & Scott's book "The Mathematical Theory of Finite Element Methods", even though a hint is provided in the book. Could you please provide some help? Many thanks!
The original exercise is as below.
Exercise 1.x.11 Show that the condition in Example 1.2.6 implies that
$$ \lim_{r\rightarrow 0} r^{n-1} |\rho(r)| = 0. $$
Example 1.2.6 Let $\rho$ be a smooth function defined for $0 < r \leq 1$ satisfying
$$ \int_0^1 |\rho'(r)|r^{n-1} \; {\rm d} r < \infty. $$