Problem $3$: Evaluating Limits $(17$ points$)$

A square is changing size over time. At time $t,$ the side length of the square is given by $s(t).$ The graph of $s$ is given in the figure below. Denote by $A(t)$ the area of the square at time $t.$

For each of the limits below, give the form of the limit$,$ then evaluate the limit$.$ Show your work and justify your answer.

a$)$ points