\(\displaystyle \lim_{t\to 0}\left[\frac{1}{t}-\frac{1}{t^{2}+t}\right]=\frac{1}{t}-\frac{1}{t(t+1)}=\frac{(t+1)}{(t+1)}\cdot \frac{1}{t}-\frac{1}{t(t+1)}=\frac{1}{t+1}\)
Now, we merely have \(\displaystyle \lim_{t\to 0}\frac{1}{t+1}\)
Can you see what the limit is now?. Since the function is continuous, just sub in x=0.
