91Ó°ÊÓ

Use tables of values to make educated guesses for each of the limits in Exercises 39–52.

$\underset{x→2}{\lim }\frac{1}{x^2-4}$

Calculate each limit in Exercises 35-80.

$\underset{x→∞}{\lim }\left(-3x^5+4x+11\right)$

For each limit statement in Exercises $41-44$, use algebra to find $\mathrm{δ}$or $N$in terms of $\mathrm{Î\mu }$or $M$, according to the appropriate formal limit definition.

$\underset{x→∞}{\lim }\frac{x-1}{x}=1$, find$N$in terms of$\mathrm{Î\mu }$.

Write each limit in Exercises 19–42 as a formal statement involving$\mathrm{δ},\mathrm{Î\mu },N,\mathrm{and}/\mathrm{or}M,$ and sketch a graph that illustrates the roles of these constants. In the last six exercises you may take function to be any appropriate graph.

$\underset{x→∞}{\lim }f\left(x\right)=-∞$

Calculate each of the limits in Exercises $29-70$.

$\underset{x→1^{+}}{\lim }\frac{1-\sqrt{x}}{1-x}$.

Indeterminate forms: Identify which of the limit forms listed here are indeterminate. For each form that is not indeterminate, describe the behavior of a limit of that form.

$∞-∞$.

In Exercises 39–44, use Theorem 1.16 and left and right limits to determine whether each function f is continuous at its break point(s). For each discontinuity of f, describe the type of discontinuity and any one-sided discontinuity.

$f\left(x\right)=\left\{\begin{array}{c}\sqrt{-x},ifx<0\\ 2,ifx=0\\ \sqrt{x},ifx>0\end{array}\right..$

Calculate each limit in Exercises 35-80.

$\underset{x→-∞}{\lim }\left(5-2x+3x^3\right)$

Use tables of values to make educated guesses for each of the limits in Exercises 39–52.$\underset{x→1}{\lim }\frac{1}{1-x}.$

Calculate each limit in Exercises 35–80.

$\underset{x→-4}{lim}\frac{x^2+8x+16}{{(x+4)}^2(x+1)}$