Let $g\(\left\)(t\(\right\))=\(\frac{t-9}{\sqrt{t}\)-3}$.
Make two tables, one showing values of $g$ for $t=8.9,8.99$, and $8.999$ and one showing values of $g$ for $t=9.1,9.01$, and $9.001$.

A projectile is fired vertically upward and has a position given by s(t)=−16t^2+128t+192, for 0≤t≤9.

a. Graph the position function, for 0≤t≤9.

A projectile is fired vertically upward and has a position given by s(t)=−16t^2+128t+192, for 0≤t≤9.

b. From the graph of the position function, identify the time at which the projectile has an instantaneous velocity of zero; call this time t=a.

A projectile is fired vertically upward and has a position given by s(t)=−16t^2+128t+192, for 0≤t≤9.

d. For what values of t on the interval [0, 9] is the instantaneous velocity positive (the projectile moves upward)?

A rock is dropped off the edge of a cliff, and its distance s (in feet) from the top of the cliff after t seconds is s(t)=16t^2. Assume the distance from the top of the cliff to the ground is 96 ft.

a. When will the rock strike the ground? 

Let $g\(\left\)(t\(\right\))=\(\frac{t-9}{\sqrt{t}\)-3}$.

Make a conjecture about the value of ${\(\displaystyle\]\lim\)_{t\(\to\)9}\(\frac{t-9}{\sqrt{t}\)-3}}$.

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

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

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.

Use a graph of f to estimate $\underset{x\to a}{\lim }f\left(x\right)$ or to show that the limit does not exist. Evaluate f(x) near $x=a$ to support your conjecture.

$f\left(x\right)=\frac{x-2}{\ln \mid x-2\mid }$; $a=2$