Checkpoint 3

Find each of the following limiting values. In each case, make a connection with a derivative calculation for which you already know the answer.

1. ${\displaystyle \underset{\Delta t\to 0}{lim}\frac{sin \Delta t}{\Delta t}}$

2. ${\displaystyle \underset{\Delta t\to 0}{lim}\frac{b^{\Delta t}-1}{\Delta t}}$, where ${\displaystyle b}$ is a positive number.