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Chapter 1: Q. 57 (page 108)

Write delta-epsilon proofs for each of the limit statements limx鈫�cfx=Lin Exercises 47鈥�60.

limx鈫�1x2-1x-1=2

Short Answer

Expert verified

Delta-epsilon proof is,

Whenever 0<|x-1|<未, we also have x2-1x-1-2<系.

Step by step solution

01

Step 1. Given information 

We are given,

limx鈫�1x2-1x-1=2

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.

For all x with 0<|x-1|<未, we also have x2-1x-1-2<系, so

=(x-1)(x+1)(x-1)-2=|x+1-2|=|x-1|<未=鈭�

So, whenever 0<|x-1|<未, we also have x2-1x-1-2<系.

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