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Math Help - Adv Calc lim prf

  1. #1
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    Adv Calc lim prf

    Suppose f is real. Prove if L = lim f(x) (x goes to a) exists, then abs f(x) goes to abs L, as x goes to a.

    Show that there is a funciton such that as x goes to a, abs f(x) goes to abs L, but the limit of f(x) does not exist.

    Thanks.
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  2. #2
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    One of the most useful properties of absolute value is this:
    \left| {\left| x \right| - \left| y \right|} \right| \le \left| {x - y} \right|.
    It is also one of the least known/taught.

    Using the \varepsilon ,\delta definition for limit with the above, you problem ‘falls’ into your lap.
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