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Precise Definition of a limit

  1. Sep 14, 2009 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution

    How close to 2 do we have to take x so that 5x+3 is within a distance of 0.075 from 13.
    I am confuse on how to evaluate this problem.
  2. jcsd
  3. Sep 14, 2009 #2
    You should state your question more clearly.

    A distance of 0.075 from 13 can be 13 + 0.075 or 13 - 0.075. Can you find an x such that 5x+3 evaluates to one of those two points?
  4. Sep 14, 2009 #3


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    5x+3 will be within distance 0.075 from 13 (above or below) as long as 5x+ 3 is between 13- 0.75 and 13+ 0.75 or [itex]12.25\le 5x+ 3\le 13.75[/itex]. Solve that inequality for x. How close is that to 2?
  5. Sep 14, 2009 #4
    I understand that part but how do you work the problem out?
  6. Sep 14, 2009 #5
    so x=1.85,2.15; then I would then subtract 2-1.85 and 2-2.15. my answer would be .15
  7. Sep 14, 2009 #6
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