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Chapter 1: Q. 45 (page 97)

For each limit limx鈫�cf(x)=Lin Exercises 43鈥�54, use graphs and algebra to approximate the largest value of 未such that if x鈭�(c-未,c)鈭�(c,c+未)thenf(x)鈭�(L-蔚,L+蔚).

limx鈫�5x-1=2,蔚=1

Short Answer

Expert verified

The largest value of未=3.

Step by step solution

01

Step 1. Given Information.

The given expression islimx鈫�5x-1=2,蔚=1.

02

Step 2. Explanation. 

From the given expression, we have,c=5,L=2

The limit expression can be written as a formal statement as below,

For all epsilon positive, there exists a delta positive such that if

x鈭�(5-未,5)鈭�(5,5+未)thenx-1=2鈭�(2-蔚,2+蔚)

Now, the largest value of delta is given by

x+1=L+蔚x+1=2+1x+1=32x+1=9x=8

Thus,

未=8-5未=3

03

Step 3. Conclusion. 

The largest value of未=3.

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