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Chapter 1: Q. 66 (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�(3x-5)=-鈭�

Short Answer

Expert verified

The proof of given limit limx鈫�-鈭�(3x-5)=-鈭� is,

N=M+53

Step by step solution

01

Step 1. Given information  

We are given,

limx鈫�-鈭�(3x-5)=-鈭�

02

Step 2. Writing the delta-epsilon proofs 

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

From the given limit, we get

f(x)=3x-5L=-鈭�c=-鈭�

Glven M<0, choose N=M+53.

If role="math" localid="1648036421117" x<N, we have,

3x-5>3N-5=M

So,

3N-5=M3N=M+5N=M+53

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