Chapter D, Problem 1E

To determine

To calculate:

Value of $\delta$ such that if $\left|x-2\right|<{\rm A}\delta$ then $\left|\frac{1}{x}-0.5\right|<0.2$

Answer to Problem 1E

The value of number $\delta$ is $\frac{4}{7}$ .

Explanation of Solution

Given information:

Condition given: $\left|x-2\right|<{\rm A}\delta$ then $\left|\frac{1}{x}-0.5\right|<0.2$

  

Calculation:

Consider the given function,

  $f\left(x\right)=\frac{1}{x}$

If $\left|x-2\right|<{\rm A}\delta$ then $\left|\frac{1}{x}-0.5\right|<0.2$

From the graph it is clear that $\alpha =2$

And $\delta$ lies between both sides of $\alpha$ .

So, $\delta =2-\frac{10}{7}$ or $\delta =2+\frac{10}{7}$

  $\frac{4}{7}$ or $=\frac{24}{7}$

Thus, the min $\left(4/7,24/7\right)$ is $4/7$ .

Hence the value of number $\delta$ is $\frac{4}{7}$ .