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Chapter 1: Q. 31 (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�0(3-4x)=3

Short Answer

Expert verified

未=蔚4

Step by step solution

01

Step1. Given information. 

We have been given a limit statement as limx鈫�0(3-4x)=3.

We have to find 未intermsof蔚.

02

Step 2. Use algebra 

From the given limit statement, we can identify

f(x)=3鈭�4xc=0L=3For蔚>0|(3鈭�4x)鈭�3|<蔚|3鈭�4x鈭�3|<蔚|鈭�4x|<蔚4|x|<蔚|x|<蔚4For0<|x鈭�c|<未,weget|x|<蔚4Therefore,未=蔚4

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