Q. 5 - Calculus

Question

Write down a mathematical equation that expresses the sentence “x is not equal to 5, and the distance between x and 5 is less than $0.01$.” Then write an equation that means “the distance between $f\left(x\right) \mathrm{and} -2$ is less than $0.5$.” 

Step-by-Step Solution

Answer

The required expressions are $0<|x-5|<0.01 and \left|f\right(x)+2|<0.5$

Step 1. Given Information

The given statement is “x is not equal to 5, and the distance between x and 5 is less than $0.01$.”  

Step 2. Explanation

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

$0<|x-5|<0.01$

And the other statement “the distance between $f\left(x\right) and -2$ is less than $0.5$.” can be written as,

$$\begin{gathered} \left|f\right(x)-(-2\left)\right|<0.5 \\ \left|f\right(x)+2|<0.5 \end{gathered}$$