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\)$

Suppose g(x) = {2x+1 if x≠0

5 if x=0.

Compute g(0) and lim x→0 g(x)

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\)$

Determine the following limits.

lim x→a (3x + 1)^2 − (3a + 1)^2 / x − a, where a is constant

Let $g\(\left\)(x\(\right\))=\(\frac{x^3-4x}{8\left|x-2\right|}\)$. <IMAGE>

Make a conjecture about the values of ${\(\displaystyle\]\lim\)_{x\(\to\)2^{-}}g\(\left\)(x\(\right\))}$, ${\(\displaystyle\]\lim\)_{x\(\to\)2^{+}}g\(\left\)(x\(\right\))}$, and ${\(\displaystyle\]\lim\)_{x\(\to\)2}g\(\left\)(x\(\right\))}$ or state that they do not exist.

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

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\)$