Question: Can someone help explain the following, 

$$
\lim \limits\_{t \to 0} \frac{1}{t} \int\_0^t W\_u\, du=\lim \limits\_{t \to 0} \frac{W\_0t}{t}=W\_0=0\,?
$$

Thanks!

Answer: 
$$
A-\frac{B}{C}=\frac{AC-B}{C}
$$
and, in particular,
$$
1-\frac{1}{z+1}=\frac{z+1-1}{z+1}
$$
$$\dfrac{z}{z+1}=\dfrac{z+1-1}{z+1}=\dfrac{z+1}{z+1}-\dfrac{1}{z+1}=1-\dfrac{1}{z+1}$$