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Chapter 1: Q. 5 (page 107)

Write down a mathematical equation that expresses the sentence 鈥�x is not equal to 5, and the distance between x and 5 is less than 0.01.鈥� Then write an equation that means 鈥渢he distance between role="math" localid="1648056272755" f(x)and-2is less than0.5.鈥�

Short Answer

Expert verified

The required expressions are0<|x-5|<0.01and|f(x)+2|<0.5

Step by step solution

01

Step 1. Given Information 

The given statement is鈥�x is not equal to 5, and the distance between x and 5 is less than 0.01.鈥�

02

Step 2. Explanation 

The statement 鈥�x is not equal to 5, and the distance between x and 5 is less than 0.01.鈥� can be written in mathematical expression as follows,

role="math" localid="1648056618509" 0<|x-5|<0.01

And the other statement 鈥渢he distance between f(x)and-2is less than 0.5.鈥� can be written as,

|f(x)-(-2)|<0.5|f(x)+2|<0.5

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