91Ó°ÊÓ

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.

$\underset{x→-1}{\lim }x.$

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.

$\frac{∞}{0^{+}}$

For each limit statement , use algebra to find δ > 0 in terms of $\mathrm{Î\mu }$> 0 so that if 0 < |x − c| < δ, then | f(x) − L| < $\mathrm{Î\mu }$.

$\underset{x→2}{\lim }(x^2-4x+6)=2$

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.

$\underset{x→-5}{\lim }(3x-2).$

Consider the graph of the function:

Find the limits of function.

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.

$\underset{h→0}{\lim }\frac{{\left(2+h\right)}^2-4}{h}=4$

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

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

Calculate each limit in Exercises 35-80.

$\underset{x→ 0}{\lim }\left(-4x^{-3}\right)$

Consider the graph of the function:

Find the limits of function.

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.

$\underset{h→0}{\lim }\frac{{\displaystyle \frac{1}{2+h}}-{\displaystyle \frac{1}{2}}}{h}=-\frac{1}{4}$