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Chapter 1: Q. 32 (page 107)

For each limit statement , use algebra to find 未 > 0 in terms of 蔚> 0 so that if 0 < |x 鈭� c| < 未, then | f(x) 鈭� L| < 蔚.

limx鈫�1(3x+8)=11

Short Answer

Expert verified

未=蔚3

Step by step solution

01

Step1. Given information. 

We have been given a limit statement as limx鈫�1(3x+8)=11.

We have to find 未intermsof蔚.

02

Step 2. Use algebra  

From the given limit statement, we can identify

f(x)=3x+8c=1L=11For蔚>0|(3x+8)鈭�11|<蔚|3x+8鈭�11|<蔚|3x鈭�3|<蔚3|x鈭�1|<蔚|x鈭�1|<蔚3For0<|x鈭�c|<未,weget|x鈭�1|<蔚3Therefore,未=蔚3

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