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Chapter 1: Q. 37 (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�21x=12;youmayassume未鈮�1

Short Answer

Expert verified

未=min(1,2蔚)

Step by step solution

01

Step1. Given information. 

We have been given a limit statement as limx鈫�21x=12;youmayassume未鈮�1.

We have to find 未intermsof蔚.

02

Step 2. Use algebra  

From the given limit statement, we can identify

f(x)=1xc=2L=12For蔚>01x鈭�12<蔚2鈭�x2x<蔚12|x鈭�2|<蔚|x鈭�2|<2蔚For0<|x鈭�c|<未,weget|x鈭�2|<2蔚Therefore,未=min(1,2蔚)

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Most popular questions from this chapter

Write delta-epsilon proofs for each of the limit statements limx鈫�cfx=Lin Exercises 47-60.

limx鈫�12x+4=6.

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(x3+1)=1

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0<|x-2|<0.1
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