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Chapter 1: Q. 41 (page 107)

For each limit statement, use algebra to find 未 or N in terms of 蔚or M, according to the appropriate formal limit definition.

limx鈫�鈭�2+鈥�(1+x+2)=1 find 未 in terms of 蔚.

Short Answer

Expert verified

未=蔚2

Step by step solution

01

Step1. Given information. 

We have been given a limit statement as limx鈫�鈭�2+鈥�(1+x+2)=1.

We have to find 未 in terms of 蔚.

02

Step 2. Use algebra.

From the given limit statement, we can identify

f(x)=1+x+2c=-2L=1For蔚>0|(1+x+2)鈭�1|<蔚|x+2|<蔚|x+2|<蔚2For0<|x鈭�c|<未,weget|x+2|<蔚2Therefore,未=蔚2

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