Решить предел lim x-> 0 [(e^x-1)/ln(1+2x)]

Lim x->0 [(e^x-1)/ln(1+2x)] = lim x->0 [(-1+e^x)/ln(1+2x)] =
=   lim x->0 [(d(-1+e^x)) / dx] [(d(log(1+2x) / dx] =
=  lim x->0 (1/2)*e^x(1 + 2x) = (1/2)*( lim x->0(e^x)* lim x->0(1+2x)) =
 = (1/2)*(e^( lim x->0 (x) * ( lim x->0(1+2x)) = (1/2)*( lim x->0(1+2x)) = 1/2