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Ineequalities 1+x<=e^x<=1/1-x

  1. Mar 9, 2005 #1
    friends help on this,

    Use the ineequalities 1+x<=e^x<=1/1-x for |x|<1 to show that
    lim(e^x-1)/x =
    x-0+
    lim(e^x-1)/x =1
    x-0-
    and hence deduce that
    lim(e^x-1)/x=1
    x-0
    b) Determine
    lim (x^3-1)/(x-1) if it exists.
    x-1
     
  2. jcsd
  3. Mar 9, 2005 #2

    Galileo

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    Rewrite your inequalities.
    For example:

    [tex]1+x \leq e^x[/tex]

    is the same as:

    [tex]1\leq \frac{e^x-1}{x}[/tex]

    Do the same for the other side of the inequality and use the squeeze theorem to evaluate the limit.
     
  4. Mar 10, 2005 #3

    arildno

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    Dearly Missed

    As for b), perform polynomial division first.
    Or L'Hopital's rule if you're allowed to do so.
     
    Last edited: Mar 10, 2005
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