91Ó°ÊÓ

In Problems 9–20, find the slope of the tangent line to the graph of f at the given point. Graph f and the tangent line.

$f\left(x\right)=-2x+1\mathrm{at}\left(-1,3\right)$

Repeat Problem 9 for $f\left(x\right)=4x$

In Problems 7– 42, find each limit algebraically

$\underset{x→-3}{\lim }x$

In Problems 7–16, use a table to find the indicated limit.

$10.\underset{x→0}{\lim }\frac{2-x}{x^2+4}$.

In Problems 8–12, use the accompanying graph of$y=f\left(x\right)$

Does $\underset{x→1}{\lim }f\left(x\right)$exist? If so, what is it? If not, explain why not?

True or False If f is continuous at c, then$\underset{x→c^{+}}{\lim }f\left(x\right)=f\left(c\right)$.

The function $f\left(x\right)=-3x+9$ is defined on the interval
$[0,3]$
(a) Graph f.
In (b)–(e), approximate the area A under f from $0$to $3$
as follows:
(b) Partition $[0,3]$ into three sub intervals of equal length and choose u as the left endpoint of each sub interval.
(c) Partition $[0,3]$ into three sub intervals of equal length and choose u as the right endpoint of each sub interval.
(d) Partition $[0,3]$ into six sub intervals of equal length and choose u as the left endpoint of each sub interval.
(e) Partition $[0,3]$ into six sub intervals of equal length and choose u as the right endpoint of each sub interval.
(f) What is the actual area A?

In Problems 7– 42, find each limit algebraically

$\underset{x→-2}{\lim }\left(5x\right)$

find the limit $\underset{x→3}{\lim }\frac{x^4-3x^3+x-3}{x^3-3x^2+2x-6}$

In Problems 9–20, find the slope of the tangent line to the graph of f at the given point. Graph f and the tangent line.

$f\left(x\right)=x^2+2\mathrm{at}\left(-1,3\right)$