Chapter 14: Q. 40 (page 889)

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

Short Answer

Expert verified

$\lim_{x \to 1^{-}} \frac{x^{3} - x}{x - 1} = 2$ the solution

Step by step solution

step 1.introduction

given limits
$\lim_{x \to 1^{-}} \frac{x^{3} - x}{x - 1}$

step 2.simplification of equation

given equation

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

step 3.the solution

the limit value the

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

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

Short Answer

Step by step solution

step 1.introduction

step 2.simplification of equation

step 3.the solution

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In Problems 33– 44, find the one-sided limit.limx→1-x3-xx-1

Short Answer

Step by step solution

step 1.introduction

step 2.simplification of equation

step 3.the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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