Ok new chapter. I think I under stand this stuff to a point. I have :

lim x -> 0 e^x -1 -x -(x^2/2)/ x^3 so eventually after taking the derivative of the top and bottom about 3 times i ended up with e^x/6 so the limit approaches infinite correct?

Then

lim x -> 0 (1+a/x)^bx, this one is slightly harder i can get the first derivative then i'm not sure what to do. So for the first derivative I have b(1+a/x)^bx-1*(a/x^2) then i'm lost. {edit} ok i just realized different form g(x) ln f(x) so if i do that i get b * ( -a/x^2) so -ab/x^2 would that be negative infinite then?