1. Limits and Continuity

Use the graph of $f\left(x\right)$to estimate the value of the limit or state that it does not exist (DNE).

$\lim_{x\rarr0}f\left(x\right)$

Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>

f(−1)

Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>

lim x→−1^− f(x)

Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>

lim x→−1^+ f(x)

Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>

lim x→−1 f(x)

Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>

f(1)

Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>

lim x→1 f(x)

Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>

lim x→3^− f(x)

Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>

lim x→3^+ f(x)

Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>

lim x→3 f(x)

The following table gives the position $s\left(t\right)$ of an object moving along a line at time $t$. Determine the average velocities over the time intervals $\left\lbrack1,1.01\right\rbrack$, $\left\lbrack1,1.001\right\rbrack$, and $\left\lbrack1,1.0001^{}\right.]$. Then make a conjecture about the value of the instantaneous velocity at $t=1$. <IMAGE>

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.

$\left\lbrack1,4\right\rbrack$

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.

$\left\lbrack1,2\right\rbrack$