在Ingersoll "thoery of financial decision making"第24页，

One commonly used form of additive utility functon is a sum of power
founctions. These utility functions can all be written as f(x)=sum(ai*(xi^r)
)/r. 这里的小写i是indicator, i=1,2,3,......

These include linear r=1(这很容易） and log-linear r=0, f(x)=sum(ai*log(xi))
, as limitting cases.

可是为什么r=0时function可以写成log的形式，在这里洛毕达法则应该不适用，因为取
极限时，分子为ai*1, 分母为0. 是不是有别的trick?能帮我看看吗？谢谢。