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Chapter 1: Q. 46 (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)a.

limx鈫�5x-1=2,蔚=0.2

Short Answer

Expert verified

The largest value of 未=1.16.

Step by step solution

01

Step 1. Given Information.

The given expression is limx鈫�5x-1=2,蔚=0.2.

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

localid="1648205138827" x鈭�(5-未,5)鈭�(5,5+未)thenx-1鈭�(2-蔚,2+蔚)

Now, the largest value of delta is given by

localid="1648204155897" x+1=L+蔚x+1=2+0.2x+1=2.22x+1=4.84x=4.84-1x=3.84

Thus,

localid="1648204285366" 未=5-3.84未=1.16

03

Step 3. Conclusion.  

The largest value of未=1.16.

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