Remember the toy car with distance function $d\left(t\right) = 10t^{2}$? Remember to label your answers with the proper units.

1. Calculate the velocity of the car at $1$ second, that is, evaluate $d ^\prime\left(1\right)$.

   Step (a):

   $d ^\prime(1)=\lim \limits_{h\to 0}\frac{10(1+h)^{2}-10(1)^{2}}{h}$

2. Calculate the velocity of the car at $3$ seconds, or $d ^\prime\left(3\right)$.

   Step (b):

   $d ^\prime(3)=\lim \limits_{h\to 0}\frac{10(3+h)^{2}-10(3)^{2}}{h}$

3. Calculate the velocity of the car at $s$ seconds for any fixed time $s$, or $d ^\prime(s)$.

   Step (c):

   $d ^\prime(s)=\lim \limits_{h\to 0}\frac{10(s+h)^{2}-10s^{2}}{h}$