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Chapter 0: Q. 48 (page 1)

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=12

Short Answer

Expert verified

The largest value of未=蟺6.

Step by step solution

01

Step 1. Given Information.

The given expression is limx鈫�蟺sinx=0,蔚=12.

02

Step 2. Explanation. 

From the given expression, we have,c=蟺,L=12.

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+12sinx=12x=蟺6

Thus,

未=蟺6-0未=蟺6

03

Step 3. Conclusion.

The largest value of未=蟺6.

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