Salut,
[tex]\lim\limits_{x\to 0}\dfrac{3^x-1}{x^2+3x}=\lim\limits_{x\to 0}\left(\dfrac{3^x-1}{x}\cdot\dfrac{x}{x^2+3x}\right)=\\\\\\=\lim\limits_{x\to 0}\left(\dfrac{3^x-1}{x}\cdot\dfrac{1}{x+3}\right)=ln3\cdot\dfrac{1}{0+3}=\dfrac{ln3}3.[/tex]
Green eyes.