Definitions of a limit

Question

Use the graph of f(x)=1x below to find a number δ such that |f(x)−0.5|<0.1 whenever 0<|x−2|<δ.

 

 

Enter the exact answer.

 

δ= ____________

Answer 1

Joaquin

Whenever the distance of x from 2 is less than delta, the difference of the function from 0.5 has to be less than 0.1

Clearly looking at the graph the difference will be less than 0.1 when the x value is in the interval between the two red vertical lines on the x axis.

So we find x when y = 0.6, y = 1/x so x = 1 / y = 1/ 0.6 = 10 / 6

We find x when y = 0.4, x = 1 / y = 1 / 0.4 = 10 / 4

Then delta is going to be the minimum of ( 2 - 10/6, 10/4 - 2 ).

Mike