Genral formua to solve this kind of question
lim f(x)^g(x) such that f(x)->1 and g(x)->infinite then the ans can directly be calculated by the formula
=e(f(x)-1)*g(x)
in this case ,the ans is e(1-x-1)*(1/x)=e-1
This formula can be applied anywhere where the form of ques is (1)infinite