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Chapter 1: Q. 51 (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="1648028930198" x鈭�(c-未,c)鈭�(c,c+未)thenf(x)鈭�(L-蔚,L+蔚).

localid="1648029006873" limx鈫�32-x2=-7,蔚=0.01

Short Answer

Expert verified

The largest value of未鈮�0.00167.

Step by step solution

01

Step 1. Given Information.

The given expression is limx鈫�32-x2=-7,蔚=0.01.

02

Step 2. Explanation. 

From the given expression, we have,c=3,L=-7

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�(3-未,3)鈭�(3,3+未)then2-x2=-7鈭�(-7-蔚,-7+蔚)

Now, the largest value of delta is given by,

localid="1648202643668" 2-x2=L+蔚2-x2=-7-0.012-x2=-7.012+7.01=x29.01=x2x=9.01

Thus,

localid="1648202678785" 未=9.01-3未鈮�0.00167

03

Step 3. Conclusion.

The largest value of未鈮�0.00167.

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Most popular questions from this chapter

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