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.

$\underset{x→0}{\lim }{x}^{-3}.$

Consider the graph of the function:

Find the limits of function.

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| < $\mathrm{Î\mu }$.

$\underset{x→3}{\lim }\frac{1}{x}=\frac{1}{3};\mathrm{you}\mathrm{may}\mathrm{assume}\mathrm{δ}≤1$

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

$\underset{x→-3}{\lim }\frac{3x^2+8x-3}{x+3}$.

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

$\underset{x→-5}{\lim }\sqrt{x}.$

Calculate each limit in Exercises 35-80.

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

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.

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

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.

${∞}^1.$

Consider the graph of the function:

Find the limits of function.

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| < $\mathrm{Î\mu }$.

$\underset{x→3}{\lim }(x^2-2x-3)=0;\mathrm{you}\mathrm{may}\mathrm{assume}\mathrm{δ}≤1$