need to find:

Question

lim as x -> 0

of

4(e^2x - 1) / (e^x -1)

Try splitting the limit for the numerator and denominator
lim lim
x->0 4(e^2x-1) (4)x->0 (e^2x-1)
______________ = ________________
lim lim
x->0 e^X-1 x->0 e^x-1

Next solve for lim x->0 and simplify