The position of an object moving vertically along a line is given by the function $s\(\left\)(t\(\right\))=-4.9t^2+30t+20$. Find the average velocity of the object over the following intervals.
$\(\left\[\lbrack\)0,3\(\right\]\rbrack\)$

Given the function $f\(\left\)(x\(\right\))=-16x^2+64x$, complete the following. <IMAGE>

Find the slopes of the secant lines that pass though the points $\(\left\)(x,f\(\left\)(x\(\right\))\(\right\))$ and $\(\left\)(2,f\(\left\)(2\(\right\))\(\right\))$, for $x=1.5,1.9,1.99,1.999,$ and $1.9999$ (see figure).

Given the function $f\(\left\)(x\(\right\))=-16x^2+64x$, complete the following. <IMAGE>

Make a conjecture about the value of the limit of the slopes of the secant lines that pass through $\(\left\)(x,f\(\left\)(x\(\right\))\(\right\))$ and $\(\left\)(2,f\(\left\)(2\(\right\))\(\right\))$ as $x$ approaches $2$.

The position of an object moving vertically along a line is given by the function $s\(\left\)(t\(\right\))=-16t^2+128t$. Find the average velocity of the object over the following intervals.

$\(\left\[\lbrack\)1,4\(\right\]\rbrack\)$

The position of an object moving vertically along a line is given by the function $s\(\left\)(t\(\right\))=-16t^2+128t$. Find the average velocity of the object over the following intervals.

$\(\left\[\lbrack\)1,2\(\right\]\rbrack\)$

The position of an object moving vertically along a line is given by the function $s\(\left\)(t\(\right\))=-4.9t^2+30t+20$. Find the average velocity of the object over the following intervals.

$\(\left\[\lbrack\)0,h\(\right\]\rbrack\)$, where $h\(\gt{0}\)$ is a real number

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

${\lim }_{x\to 1^{-}}f\left(x\right)$

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

${\lim }_{x\to 1^{+}}f\left(x\right)$

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

a. f(1)