   Chapter 2, Problem 3P ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Evaluate lim x → 0 | 2 x − 1 | − | 2 x + 1 | x .

To determine

To evaluate: The value of limx0|2x1||2x+1|x.

Explanation

Definition used:

An absolute function |x| is defined as follows.

|x|={x if x<0x if x0.

Calculation:

Obtain the value of the limit of the function limx0|2x1||2x+1|x.

Consider the function f(x)=|2x1||2x+1|x.

From the definition of absolute function,

|2x1|={(2x1)  if  2x1<0    2x1    if  2x10 and |2x+1|={(2x+1)     if  2x+1<0(2x+1)  if  2x+10

This follows that,

|2x1|={(2x1)  if  x<12    2x1    if  x12 and |2x+1|={(2x+1)  if  x<12   2x+1     if  x12

This implies that, |2x1||2x+1| is defined in the interval 12<x<12 as x approaches zero

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