91Ó°ÊÓ

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

True or False Every polynomial function is continuous at every real number.

In Problems 7– 42, find each limit algebraically

$\underset{x→4}{\lim }(-3x)$

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

$12.\underset{x→3}{\lim }=\frac{x^2-9}{x^2-3x}$.

Determine whether $f$is continuous at each of the following numbers. If it is not, explain why not.

$\left(a\right)x=-2\left(b\right)x=1\left(c\right)x=3\left(d\right)x=4$

Repeat Problem 11 for $f\left(x\right)=-2x+8$

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.

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

In Problem, determine whether f is continuous at c.

$f\left(x\right)=3x^4-x^2+2,c=5$

In Problem, determine whether f is continuous at c.

$f\left(x\right)=\frac{x^2-4}{x+2},c=-2$

In Problems 7– 42, find each limit algebraically

$\underset{x→2}{\lim }\left(5x^4\right)$