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Chapter 1: Q. 3 (page 152)

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

For 未>0,x鈭�(c-未,c)鈭�(c,c+未)if and only if 0<<未.

Short Answer

Expert verified

For 未>0,x鈭�(c-未,c)鈭�(c,c+未)if and only if0<|x-c|<未.

Step by step solution

01

Step 1. Given information. 

The given incomplete statement is the following.

For 未>0,x鈭�(c-未,c)鈭�(c,c+未)if and only if 0<<未.

02

Step 2. Explanation. 

x鈭�(c-未,c)鈭�(c,c+未)can be elaborate asc-未<x<c+未.

Subtract c from all.

c-未-c<x-c<c+未-c-未<x-c<+未x-c<未

So the completer statement is the following.

For 未>0,x鈭�(c-未,c)鈭�(c,c+未)if and only if 0<|x-c|<未.

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