CPM Homework Help : PC3 Problem 13-129

Suppose that the distance traveled by a toy car in the first $t$ seconds is $d\left(t\right) = 20t^{2}$ . What is the velocity of the car at time $t$ ?

Step (1):

$v\left(t\right)=d^\prime(t)=\lim \limits_{h \to 0} \frac{d(t+h)-d(t)}{h}$

Step (2):

$\lim \limits_{h \to 0} \frac{20(t+h)^{2}-20t^{2}}{h}$