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Chapter 1: Q. 63 (page 108)

For each of the limit statements in Exercises 61-66, write a 未-M,N-系, or N-M proof, according to the type of limit statement.
limx鈫�鈭�2x-1x=2

Short Answer

Expert verified

The proof of given limitlimx鈫�鈭�2x-1x=2 is,

N=1蔚

Step by step solution

01

Step 1. Given information  

We are given,

limx鈫�鈭�2x-1x=2

02

Step 2. Writing the delta-epsilon proofs 

The strategy is to use algebra to find N in terms of 蔚 ,

From the given limit, we get

f(x)=2x-1xc=鈭�L=2

Given 蔚>0, choose N=1蔚.

If x>N, we have,

role="math" 2x-1x-2=2x-1-2xx=-1x=1x<1N=蔚

Hence,N=1蔚

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