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Chapter 1: Q. 49 (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 localid="1648028606662" x鈭�(c-未,c)鈭�(c,c+未)thenf(x)鈭�(L-蔚,L+蔚).

localid="1648028619268" limx鈫�01-cosxx=0,蔚=12

Short Answer

Expert verified

The largest value of未鈮�1.11.

Step by step solution

01

Step 1. Given Information.

The given expression is limx鈫�01-cosxx=0,蔚=12.

02

Step 2. Explanation. 

From the given expression, we have, c=0,L=0

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�(0-未,0)鈭�(0,0+未)then1-cosxx鈭�(0-蔚,0+蔚)

Now, the largest value of delta is given by,

localid="1648206479588" 1-cosxx=L+蔚1-cosxx=0+121-cosxx=12x=2-2cosxx鈮�1.11

Thus,

未=1.11-0未鈮�1.11

03

Step 3. Conclusion. 

The largest value of未鈮�1.11

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