I can calculate this limit:
Limit[(c^(1 - g) - 1)/(1 - g), g -> 1]
and obtain the correct value:
but if I try to use a transformation rule (e.g. to plot that function for different values of g), I get an Indeterminate result:
Limit[(c^(1 - g) - 1)/(1 - g), g -> d] /. d -> 1
I would assume that the transformation rule applies BEFORE the limit is calculated, but apparently that's not the case; and, on the other hand, I don't know how to force Mathematica to apply the rule before the limit is calculated.