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Chapter 10: Q. 4 (page 777)

Fill in the blanks to complete each of the following theorem statements:

For 蔚>0,f(x)鈭�(L-蔚,L+蔚)if and only if<蔚.

Short Answer

Expert verified

For 蔚>0,f(x)鈭�(L-蔚,L+蔚)if and only ifrole="math" localid="1648287054505" f(x)-L<蔚.

Step by step solution

01

Step 1. Given information. 

The given incomplete statement is the following.

For 蔚>0,f(x)鈭�(L-蔚,L+蔚)if and only if<蔚.

02

Step 2. Explanation. 

f(x)鈭�(L-蔚,L+蔚)can be elaborate as L-蔚<f(x)<L+蔚

Subtract L from all.

L-蔚-L<f(x)-L<L+蔚-L-蔚<f(x)-L<+蔚f(x)-L<蔚

So the completed statement is the following.

For 蔚>0,f(x)鈭�(L-蔚,L+蔚)if and only if f(x)-L<蔚.

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