3. The equation for the luminosity function defined by Schechter is:
$\Phi(L)dL = N_0 \left(\frac{L}{L_*}\right)^\alpha \exp\left(-\frac{L}{L_*}\right)\frac{dL}{L_*}$
(a) For the faintest galaxies, $L << L_*$. Show that in that case the Schechter function is a
power law.
(b) Considering only this regime of the faint galaxies, compute the total luminosity emitted
by galaxies between luminosities $L_{min}$ and $L_{max}$. Compute this for values of $\alpha$ of -1, -2
and -3. Discuss which galaxies dominate the luminosity in this regime for the different
values of $\alpha$.
