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Chapter 1: Q. 61 (page 108)

For each of the limit statements in Exercises 61-66, write a 未-M,N-系, or N-Mproof, according to the type of limit statement.

limx鈫�-2+1x+2=鈭�

Short Answer

Expert verified

Delta-epsilon proof is,

未=1M

Step by step solution

01

Step 1. Given information  

We are given,

limx鈫�-2+1x+2=鈭�

02

Step 2. Writing the delta-epsilon proofs 

The strategy is to use algebra to find 未 in terms of M,

From the given limit, we get

f(x)=1x+2c=-2L=鈭�

Given M>0, choose 未=1M.

If x鈭�(-2,-2+未), we have 0<x+2<未,

Now for 未>0,

role="math" |x-(-2)|<未|x+2|<未1|x+2|<1未<M

Hence,

未=1M

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