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Chapter 1: Q. 47 (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�蟺sinx=0,蔚=22

Short Answer

Expert verified

The largest value of 未=蟺4.

Step by step solution

01

Step 1. Given Information.

The given expression is limx鈫�蟺sinx=0,蔚=22.

02

Step 2. Explanation. 

From the given expression, we have,c=蟺,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�(蟺-未,蟺)鈭�(蟺,蟺+未)thensinx鈭�(0-蔚,0+蔚)

Now, the largest value of delta is given by,

sinx=L+蔚sinx=0+22sinx=22x=蟺4

Thus,

未=蟺4-0未=蟺4

03

Step 3. Conclusion. 

The largest value of未=蟺4.

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