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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 14: Q. 9 (page 905)

find the limit $\lim_{x 鈫� - 1} \frac{x^{2} - 1}{x^{3} - 1}$

Short Answer

Expert verified

$\lim_{x 鈫� - 1} \frac{x^{2} - 1}{x^{3} - 1} = 0$

Step by step solution

01

Step 1. Given information

$\lim_{x 鈫� - 1} \frac{x^{2} - 1}{x^{3} - 1}$

02

Step 2. limit of the function

We can find limit of rational function by $\lim_{x 鈫� c} f (x) = f (c)$ f c is in the domain of f(x) and the domain of f(x)= $\frac{x^{2} - 1}{x^{3} - 1}$ is all real number except 1

Here c= -1 and is in the domain. So,

$\lim_{x 鈫� - 1} \frac{x^{2} - 1}{x^{3} - 1} = \frac{(- 1)^{2} - 1}{(- 1)^{3} - 1} = \frac{1 - 1}{- 1 - 1} = 0$

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Most popular questions from this chapter

True or False The exponential function $f (x) = e^{x}$ is increasing on the interval $(- 鈭�, 鈭�)$ . (p. 280)

True or False The limit of a rational function at $5$ equals the value of the rational function at $5$

True or False Some rational functions have holes in their graph.

In Problems 45-60, determine whether $f$ is continuous at $c$ .

$f (x) = x^{3} - 3 x^{2} + 2 x - 6, c = 2$

Graph each function. Use the graph to find the indicated limit, if it exists.

$\lim_{x 鈫� \frac{蟺}{2}} f (x), f (x) = \sin (x)$

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