## Calculus (3rd Edition)

Instantaneous velocity=$\lim\limits_{\Delta t \to 0}$(average velocity) $=\lim\limits_{\Delta t \to 0}\frac{\Delta s}{\Delta t}$ For the time interval [3, 3.1], $\frac{\Delta s}{\Delta t}=\frac{4.9(3.1)^{2}-4.9(3)^{2}}{3.1-3}=29.89$ For the time interval [3, 3.01], $\frac{\Delta s}{\Delta t}=\frac{4.9(3.01)^{2}-4.9(3)^{2}}{3.01-3}=29.449$ For the time interval [3, 3.0001], $\frac{\Delta s}{\Delta t}=\frac{4.9(3.0001)^{2}-4.9(3)^{2}}{3.0001-3}=29.40049$ We see that as $\Delta t$ tends to 0, $\frac{\Delta s}{\Delta t}$ tends to 29.4. That is, at t=3, $\lim\limits_{\Delta t \to 0}\frac{\Delta s}{\Delta t}=29.4\,m/s$