1. Limits and Continuity

Consider the position function s(t)=−16t^2+128t (Exercise 13). Complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t=1. <IMAGE>

Consider the position function s(t)=−16t^2+100t. Complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t=3. <IMAGE>

Use the graph of $h$ in the figure to find the following values or state that they do not exist. <IMAGE>

$h\left(2\right)$

Use the graph of $h$ in the figure to find the following values or state that they do not exist. <IMAGE>

$h\left(4\right)$

Use the graph of $h$ in the figure to find the following values or state that they do not exist. <IMAGE>

${\displaystyle\lim_{x\to4}h\left(x\right)}$

Use the graph of $g\left(x\right)$ in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. <IMAGE>

$\lim_{x\to2}g\left(x\right)$

Use the graph of g(x) in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. <IMAGE>

${\lim }_{x\to 4}g\left(x\right)$

Use the graph of $g$ in the figure to find the following values or state that they do not exist. <IMAGE>

${\displaystyle\lim_{x\to0}g\left(x\right)}$

Use the graph of $f$ in the figure to find the following values or state that they do not exist. <IMAGE>

$f\left(1\right)$

Use the graph of $f$ in the figure to find the following values or state that they do not exist. <IMAGE>

$f\left(0\right)$

Let $f\left(x\right)=\frac{x^2-4}{x-2}$ . <IMAGE>

Calculate $f\left(x\right)$ for each value of $x$ in the following table.

Let $f\left(x\right)=\frac{x^2-4}{x-2}$. <IMAGE>

Make a conjecture about the value of ${\displaystyle\lim_{x\to2}\frac{x^2-4}{x-2}}$.

The function $s(t)$ represents the position of an object at time t moving along a line. Suppose $s(2)=136$ and $s(3)=156$ . Find the average velocity of the object over the interval of time $[2, 3]$ .

The table gives the position s(t)of an object moving along a line at time t, over a two-second interval. Find the average velocity of the object over the following intervals. <IMAGE>

a. $[0, 2]$

The table gives the position s(t)of an object moving along a line at time t, over a two-second interval. Find the average velocity of the object over the following intervals. <IMAGE>

c. $[0, 1]$