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Limit prove using definition

  1. Jul 4, 2013 #1
    1. The problem statement, all variables and given/known data
    Hello, I have to prove, using the limit definition, that [itex]\lim_{x\to 1^{+}}{\frac{x-3}{x-1}}=-\infty[/itex]

    3. The attempt at a solution
    I've set this unequation [itex]\frac{x-3}{x-1} < - M[/itex] but it doesn't lead to the result [itex]1<x<1+\frac{2}{M+1}[/itex], what did I wrong ?

  2. jcsd
  3. Jul 4, 2013 #2


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    Science Advisor

    You do understand that we can't tell you what you did wrong if you don't tell us what you did, don't you?
  4. Jul 4, 2013 #3
    I've set up this unequation [itex]\frac{x-3}{x-1} < - M[/itex] to prove the limit using its definition but it doesn't lead to the result [itex]1<x<1+\frac{2}{M+1}[/itex]
  5. Jul 4, 2013 #4


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    Homework Helper

    Hint: ##M+3 = (M+1) + 2##.
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