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\)0,3\(\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\)1,4\(\right\]\rbrack\)$

Determine the following limits.

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

Determine the following limits.

lim h→0 (h + 6)^2 + (h + 6) − 42 / h

Graph the function f(x)=e^−x / x(x+2)^2 using a graphing utility. (Experiment with your choice of a graphing window.) Use your graph to determine the following limits.

d. lim x→0^+ f(x)

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.