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## Homework Statement

*How close is [itex]x[/itex] to [itex]x_0[/itex] ([itex]x_0 \neq 0[/itex]) so that*

2. Homework Equations

2. Homework Equations

## The Attempt at a Solution

I tried to use absolute value properties:[tex]- \epsilon \lt \frac{\sqrt{x_0^2+1}}{x_0^3} - \frac{\sqrt{x^2+1}}{x^3} \lt \epsilon[/tex]By adding in the three sides, we have:[tex]\frac{\sqrt{x^2+1}}{x^3} - \epsilon \lt \frac{\sqrt{x_0^2+1}}{x_0^3} \lt \frac{\sqrt{x^2+1}}{x^3} + \epsilon[/tex]But that doesn't say anything about the distance between the terms in the absolute value, and I don't know how to algebrically organize the inequality to achieve that. I'd greatly appreciate some help!