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Chapter 1: Q. 59 (page 108)

Write delta-epsilon proofs for each of the limit statements in Exercises 47鈥�60.

limx鈫�5+x-5=0

Short Answer

Expert verified

Delta-epsilon proof is,

Whenever x鈭�(5,5+未), we also have |x-5-0|<鈭�.

Step by step solution

01

Step 1. Given information  

We are given,

limx鈫�5+x-5=0

02

Step 2. Writing the delta-epsilon proofs 

The strategy is to write delta-epsilon proofs for the given limit statement.

Consider that 鈭�>0, choose 未=系2.

The limit statement limx鈫�5+x-5=0means that for all 鈭�>0, there exist 未>0such that if x鈭�(5,5+未), then |x-5-0|<系.

5<x<5+未5-5<x-5<5+未-50<x-5<未

This means that, when localid="1648029258219" 0<x-5<未, we have

|x-5-0|=|x-5|=x-5<未=鈭�2=鈭�

So, whenever x鈭�(5,5+未), we also have |x-5-0|<鈭�.

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Most popular questions from this chapter

Use algebra to find the largest possible value of 未 or smallest possible value of N that makes each implication true. Then verify and support your answers with labeled graphs.

Ifx>N, then1x2鈭�0<0.001

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Write each of the inequalities in interval notation:

fx-L<鈭�

Write delta-epsilon proofs for each of the limit statements in Exercises 47鈥�60.

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