- #1

WK95

- 139

- 1

## Homework Statement

Prove the following:

lim x

^{2}- x = 0

x→1

## Homework Equations

If 0<|x-a|<δ then |f(x)-L|<ε

## The Attempt at a Solution

Part I - Set up

0<|x-a|<δ |f(x)-L|<ε

If 0<|x-1|<δ then |(x^2 - x) - 0|<ε

x|x-1|<ε

x|x-1|<ε

|x-1|<ε/x

δ=ε/x

Part II - Proof

Given ε < 0, choose δ=ε/x

If 0<|x-1|<δ then

|(x^2 - x) - 0| = |x^2 - x| = x|x - 1| < xδ = x(ε/x) = ε