Answer
The limit of the average rate of change for $g(t)$ at $t=t_0$ is as follows:
$\lim\limits_{h \to 0}\dfrac{Δy}{Δx}=\lim\limits_{h \to 0}\dfrac{g(t_0+h)−g(t_0)}{h}$.
Work Step by Step
In order to compute the rate of change of the function $y=g(t)$ at $t=t_0$, we will find a limit of the average rate of change.
We know that the average rate of change formula for $y=g(t)$ over the interval from $t=t_0$ to $t=t_1$ and $t_1−t_0=h$ can be expressed as:
$\dfrac{Δy}{Δx}=\dfrac{g(t_1)−g(t_0)}{(t_1−t_0)}=\dfrac{g(t_0+h)−g(t_0)}{h}$
Thus, we can interpret from the above discussion that the limit of the average rate of change for $g(t)$ at $t=t_0$ is:
$\lim\limits_{h \to 0}\dfrac{Δy}{Δx}=\lim\limits_{h \to 0}\dfrac{g(t_0+h)−g(t_0)}{h}$
