Solve $\lim_\limits{x\to 0}\frac {e^{3x}-1}{e^{x}-1} $ I have problem with  $$\lim_{x\to 0}\frac {e^{3x}-1}{e^{x}-1} $$
I have no idea what to do first. 

Hint:
Use equivalents:
$$\mathrm e^{ax}-1\sim_0 ax,\quad\text{hence}\quad \frac{\mathrm e^{ax}-1}{\mathrm e^x-1}\sim_0 \frac{ax}x=a.$$
Alternative hint:
$$\frac{\mathrm e^{ax}-1}{x}\xrightarrow[x\to0]{}(\mathrm e^{ax})'\,\Big\lvert_{x=0}$$
