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Finding the value of delta

  1. Oct 12, 2009 #1
    1. The problem statement, all variables and given/known data

    Suppose f(x) = x2 + x + 1, a = 1, and L = 3. Find a value d > 0 such that 0 < |x - a| < d implies |f(x) - L| < 1/100

    2. Relevant equations



    3. The attempt at a solution

    Given 0<|x-1|<d implies 0<|x2 + x + 1 - 3|<1/100

    0< x2 + x + -2 <1/100
    0<(x+2)(x-1)<1/100

    Assume
    0<|x-1|<1
    1<x<2
    3<x+2<4

    Then
    3|x-1| < (x+2)|x-1| < 4|x-1| < 1/100

    We need
    4|x-1| < 1/100
    |x-1| < 1/25


    1/25 < 1, therefore d should be 1/25.
     
  2. jcsd
  3. Oct 12, 2009 #2
    In the second step it should be 0<x<2.
     
  4. Oct 12, 2009 #3
    Ok.
    But that doesn't really affect the rest does it?
     
  5. Oct 12, 2009 #4
    The 3 should be a 2 in the next two statements following that. Also, d should be 1/400 because you divide 1/100 by 4. You accidently multiplied by 4. Other than that, it looks good.
     
  6. Oct 12, 2009 #5
    Oh oops lol.
    Ok thanks.
     
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