Chapter 14: Q. 41 (page 889)

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

Short Answer

Expert verified

The value of limit is

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

Step by step solution

step 1.introduction

Given limit

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

step 2.equation simplification

consider the equation

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

step 3.the solution

the limit value

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

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

Short Answer

Step by step solution

step 1.introduction

step 2.equation simplification

step 3.the solution

One App. One Place for Learning.

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In Problems 33– 44, find the one-sided limit.limx2-1x3+1x→1-

Short Answer

Step by step solution

step 1.introduction

step 2.equation simplification

step 3.the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Logic and Functions

Theoretical and Mathematical Physics

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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