Hans Georg Schaathun
August 2016
$$ h(t) = 10 - 4{,}9t^2 $$
$$ \bar v(t,\Delta t) = \frac{\Delta h}{\Delta t} \quad\text{ if } \Delta t\neq 0 $$
$$\bar v(t,\Delta t) =- 4{,}9(2t+\Delta t)$$
$$ v(t) = \lim_{\Delta t\to0} \bar v(t,\Delta t) $$
$$ v(t) = - 4{,}9\cdot 2t = - 9{,}8t $$
$$ v(t) = \lim_{\Delta t\to\infty} \frac{\Delta h}{\Delta t} = h'(t) $$
$$ h'(t) = \lim_{\Delta t\to0} \frac{h(t+\Delta t)-h(t)}{\Delta t} $$