- #1

Mr Davis 97

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## Homework Statement

Prove that ##f(x) = \frac{1}{x}## is continuous using the epsilon-delta definition of continuity.

## Homework Equations

## The Attempt at a Solution

We will assume that the domain of ##f## is ##\mathbb{R} / \{ 0\}##. Let ##x_0## be in the domain. First, we look at ##\displaystyle |f(x) - f(x_0)| = \frac{|x-x_0|}{|x||x_0|}##. The problem I now see is with the denominator. We need to get a bound for ##\frac{1}{|x|}## that does not depend on ##x##. I am not exactly sure how I would go about doing this... Any tips?