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Chapter 1: Q. 81 (page 122)

Write a delta鈥揺psilon proof that shows that the function f(x)=3x-5is continuous at x=2. (This exercise depends on Section 1.3.)

Short Answer

Expert verified

Hence we provedlimx鈫�23x-5=1.

Step by step solution

01

Step 1. Given Information

We are given the function f(x)=3x-5is continuous at x=2and we need to write a delta鈥揺psilon proof.

02

Step 2. Delta–epsilon proof 

f(x)=3x-5c=2L=3(2)-5=6-5=1

For 蔚>0,未=蔚3,

If 0<x-2<未we have,

role="math" localid="1648196824344" 3x-5-1=3x-6=3x-2<3未=3蔚3=蔚鈭�limx鈫�23x-5=1

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