Finding Delta

[Latty-mir]

I have been studying this subject for two days now in a college environment. I thought I understood it, but now I am drawing a blank again. Could you please help?

My problem is this:

The graph of F(x)=2-(1/x) is shown in the figure. Find delta (symbol) such that 0<(abs val x-1)<delta then (absVal F(x) -1)<0.1.

On the graph, on the y-axis starting from the top are values : 1.1, 1, 0.9. The 1 coincides with the 1 on the x-axis. I don't know any other values.

Please help me...

 

[HallsofIvy]

Another way to do this is to note that "|F(x)- 1|< 0.1" is the same as \(\displaystyle \left|2- \frac{1}{x}- 1\right|< 0.1\).
\(\displaystyle \left|1- \frac{1}{x}\right|= \left|\frac{x- 1}{x}\right|< 0.1\)
Since |x| is always positive, we can multiply by it on both sides:
\(\displaystyle \left|x- 1\right|< 0.1|x|\)
Of course we are interested in what happens when x is close to 1 so we can assume |x|< 2. That means that \(\displaystyle \left|x- 1\right|< 0.1x< 0.2\). So take \(\displaystyle \delta\) to be any number less than or equal to 0.2.