Find $\delta$ when $\epsilon$ is known (limit problem) I had a wicked time of these limit problems on a quiz, I can't find any examples of this with the $x$ in the denominator. How do you establish the connection between $|x – 1|$ and $|f(x) – 1|$?
Find the largest $\delta$ such that if $0 < |x – 1| < \delta $, then $|f(x) – 1| < 0.1$.
$f(x) = 2 - \frac{1}{x}$

Start by writing down what $|f(x) - 1| < 0.1$ means and then solve for a range of $x$. 
$|f(x)-1| < 0.1$
$-0.1 < f(x)-1 < 0.1$
$0.9 < f(x) < 1.1$
$0.9 < 2-\dfrac{1}{x} < 1.1$
Can you find a range for $x$ that makes this true? That will help you determine what $\delta$ needs to be.
