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Homework Help: Find epsilon & delta

  1. Feb 8, 2007 #1
    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. jcsd
  3. Feb 8, 2007 #2

    quasar987

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    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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