lim

Question

x->0 (e^2x-1)/(e^x-1)

I know that the answer is 2, but how would I get 2?

Answer 1

e^2x = (e^x)^2
let z = e^x
then you have
(z^2 -1)/(z-1)
(z-1)(z+1) / (z-1)
so
z+1
e^x +1
e^0 + 1
1 + 1
about 2 all right