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Chapter 1: Q. 43 (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).

role="math" localid="1648027918805" limx鈫�2x3=8,蔚=0.5

Short Answer

Expert verified

The largest value of 未鈮�0.0408.

Step by step solution

01

Step 1. Given Information.

The given expression islimx鈫�2x3=8,蔚=0.5.

02

Step 2. Explanation.

From the given expression, we have, c=2,L=8.

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="1648188825671" x鈭�(2-未,2)鈭�(2,2+未)Thenx3鈭�(8-蔚,8+蔚)

Now, the largest value of delta is given by,

x3=L+蔚x3=8+0.5x3=8.5x=8.513

Thus,

未=8.513-2未鈮�0.0408

03

Step 3. Conclusion.

The largest value of 未鈮�0.0408.

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