Question

Hi,
I am having trouble understanding the concept of delta and epsilon. Please explain the following problem. Thank you!!

Given the function f(x)=2-(1/x), find delta such that if 0< Ix-2I < delta, then the absolute value of f(x)-1 is < 0.1

Answer 1

You want

|f(x)-1| < 0.1
|2-(1/x)-1)| < 0.1
|1 - 1/x| < 0.1
Now, let x = 2+δ
|1 - 1/(2+δ)| < 0.1
|2+δ-1| < 0.1(2+δ)
|δ+1| < 0.2 + 0.1δ
we know that δ+1 > 0, so that means
δ+1 < 0.1 + 0.1δ
0.9δ < -0.9
δ < -1

This makes no sense. Since f(1/2) = 0, I think you want |x - 1/2| < δ

So, go through the steps and you should come up with a small value for δ. You might consider this page:

http://www.wolframalpha.com/input/?i=%7C2-1%2Fx%7C+%3C+0.1