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Math Help - Proving infinate limits help!!

  1. #1
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    Proving infinate limits help!!

    I need to prove that as x-> + infinity, (x+1)/(x-1)= 1

    With epsilon delta definitions... this is so confusing, can anyone help?
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  2. #2
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    Quote Originally Posted by squintz123 View Post
    I need to prove that as x-> + infinity, (x+1)/(x-1)= 1

    With epsilon delta definitions... this is so confusing, can anyone help?
     \frac{x+1}{x-1} = \frac{x(1+\frac{1}{x})}{x(1-\frac{1}{x})}

     =  \frac{1+\frac{1}{x}}{1-\frac{1}{x}}

    What happens to the two fractions when x tends towards infinity?

    EDIT: Ah sorry, I didn't read your need for epsilon delta definitions.
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  3. #3
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    Quote Originally Posted by squintz123 View Post
    I need to prove that as x-> + infinity, (x+1)/(x-1)= 1

    With epsilon delta definitions... this is so confusing, can anyone help?
    What you want to show is that for any \epsilon > 0 there is an N > 0 such that

    \left| \frac{x+1}{x-1} - 1\right| < \epsilon when x > N

    Now start with the left

    \left| \frac{x+1}{x-1} - 1\right| < \epsilon
    \left| \frac{2}{x-1}\right| < \epsilon

    \left| \frac{x-1}{2} \right| > \frac{1}{\epsilon}
    \left| x - 1\right| > \frac{2}{\epsilon}
    or
    x-1 >\frac{2}{\epsilon} (x is very large)

    or

    x > \frac{2}{\epsilon} + 1

    This is your N, i.e. N = \frac{2}{\epsilon} + 1

    Then work the steps in reverse.
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  4. #4
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    Thank you so much man. That makes a lot more sense... My professor makes it sound so confusing...
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