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Find epsilon & delta

1. Homework Statement

find a number delta

2. Homework 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
 

Answers and Replies

quasar987
Science Advisor
Homework Helper
Gold Member
4,771
7
your equation is wrong as you suspected...

[tex]|1/x-1/2|\neq |x-2|^{-1}[/tex]

I suggest this first approach:

[tex]|1/x-1/2|=|(2-x)/2x|=|1/2x||x-2|[/tex]

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.
 

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