# Find epsilon & delta

1. Feb 8, 2007

### xviddivxoggmp3

1. The problem statement, all variables and given/known data

find a number delta

2. Relevant equations

f(x) = 1/x

| 1/x - 0.5 |<0.2 whenever | x - 2 | < delta

3. The attempt at a solution

how would you factor out a negative exponent?
is this possible?
i think i can get x out from under the 1/x with using negative exponents, but how would i factor it out? is this the wrong way to go with this?

|1/x - 1/2| < 0.2
| x - 2|^-1 < 0.2

2. Feb 8, 2007

### quasar987

your equation is wrong as you suspected...

$$|1/x-1/2|\neq |x-2|^{-1}$$

I suggest this first approach:

$$|1/x-1/2|=|(2-x)/2x|=|1/2x||x-2|$$

So that now finding delta such that |x-2|<delta ==> |1/x-1/2|<0.2 is equivalent to finding delta such that |x-2|<delta ==> |x-2|<|2x|0.2=0.4|x|

This reads "As soon as the distance from x to 2 is smaller than 0.4 times the distance from x to 0, then we have |1/x-1/2|<0.2".

Pick your favorite delta satisfying this.