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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. 41 (page 889)

In Problems 33鈥� 44, find the one-sided limit.
$\underset{x 鈫� 1^{-}}{\lim \frac{x^{2} - 1}{x^{3} + 1}}$

Short Answer

Expert verified

The value of limit is

$\underset{x 鈫� 1^{-}}{\lim \frac{x^{2} - 1}{x^{3} + 1} = \frac{- 2}{3}}$

Step by step solution

01

step 1.introduction

Given limit

$\underset{x 鈫� - 1^{-}}{\lim \frac{x^{2} - 1}{x^{3} + 1}}$

02

step 2.equation simplification

consider the equation

$= \frac{x^{2} - 1}{x^{3} + 1} = \frac{(x - 1) (x + 1)}{(x + 1) (x^{2} - x + 1)} = \frac{(x - 1)}{(x^{2} - x + 1)}$

03

step 3.the solution

the limit value

$\underset{x 鈫� - 1^{-}}{\lim \frac{x^{2} - 1}{x^{3} + 1}} = \underset{x 鈫� - 1^{-}}{\lim \frac{x - 1}{x^{2} - x + 1}} = \frac{- 1 - 1}{{(- 1)}^{2} - (- 1) + 1} = \frac{- 2}{3}$

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