- #1

madah12

- 326

- 1

## Homework Statement

prove the statement using epsilon delta definition of the limit

lim x->2 (x^3)=8

## Homework Equations

lim x->a f(x)=L is true when

|f(x)-L|<e

whenever

0< |x-a|<d

## The Attempt at a Solution

|x^3 - 8| < e

|(x-2)| |(x^2+2x+4)|<e

x^2+2x+4 has no real roots there for only has one sign f(0)=4 so it is always positive

so |x^2+2x+4|=x^2+2x+4

|(x-2)||(x^2+2x+4)| <C(x-2)<e

where

|(x^2+2x+4)|<C

(x-2) < (e/C) =d

I usually solve most problems like this but I can't find the C

I know that we usually say that d is a small distance so |x-a| <1

|x-2|<1

1<x<3

but then what exactly?