Precision of a limit

Question

Use the graph of f(x)=1x below to find a number δ such that |f(x)−0.25|<0.1 whenever 0<|x−4|<δ.

 

 

Enter the exact answer.

Answer 1

The function has to be within 0.1 units of 0.25 ie between 0.15 and 0.35.

So from the graph, the x value has to be between the x value at the red vertical line to the left of x=4, and the x value at the red vertical line to the right of x=4

Lets call these x1, x2, where x1 < 4 < x2

Then δ has to be the smallest of (4-x1) and (x2-4). [ you can figure out why]

So from the graph you can find these (measure scale on x axis , use that to find x1, x2)