It looks like the limit is
[tex]\displaystyle \lim_{x\to0} \frac{e^{3x} - 1 - 3x}{x^2}[/tex]
L'Hôpital's rule works in this case; applying it twice gives
[tex]\displaystyle \lim_{x\to0} \frac{e^{3x} - 1 - 3x}{x^2} = \lim_{x\to0} \frac{3e^{3x} - 3}{2x} = \lim_{x\to0} \frac{9e^{3x}}{2} = \boxed{\frac92}[/tex]
