Please help me on calculus: theorem

Question

Find the exact value of the following limit: 

Answer 1

lim _x→0 [(e^3x - 3x - 1)÷(x²)] results in the indeterminate form 0/0 so apply L'Hôpital's rule, resulting in

lim _x→0 [(3e^3x - 3)÷(2x)]; again, the indeterminate form 0/0 so apply L'Hôpital's rule once more, resulting in

lim _x→0 [(9e^3x)÷(2)] = 9/2.