- #1

Metal_Zelda

- 6

- 0

## Homework Statement

Prove [tex]lim_{x->\frac{1}{10}}\frac{1}{x}=10[/tex]

## Homework Equations

|f(x)-L|<epsilon, |x-a|<delta

## The Attempt at a Solution

I need to go from 1/x to x, so I applied an initial condition of delta<1/20

[tex]

\frac{-1}{20}<x-\frac{1}{10}<\frac{1}{20}[/tex]

[tex]\frac{1}{10}<x<\frac{3}{10}[/tex]

[tex]\frac{1}{x}<10

[/tex]

Moving on to the left side of the proof,

[tex]

|\frac{1}{x}-10|<\epsilon[/tex]

[tex]-\epsilon<\frac{1}{x}-10<\epsilon[/tex]

This is where I am stuck. If I use the fact that 1/x<10, I end up with -epsilon<10-10<epsilon, which isn't helpful.