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How to find double limits

  1. May 24, 2013 #1


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    Gold Member

    1. The problem statement, all variables and given/known data
    [itex]\stackrel{lim}{y→0}\left( \stackrel{lim}{x→∞} \dfrac{\left( 1+\dfrac{ay}{x} \right)^x - \left( 1+\dfrac{by}{x} \right)^x}{y} \right)[/itex]

    2. Relevant equations

    3. The attempt at a solution
    I need some hints. I really don't know how to solve these kinds of limits in which two variables are involved.
  2. jcsd
  3. May 24, 2013 #2
    Just do the inner one first with y held constant, then do the outer one. If you know how to do one-dimensional limits then these are just as easy!
  4. May 24, 2013 #3


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    Science Advisor

    You need to know that [itex]\lim_{x\to \infty}\left(1+ \frac{a}{x}\right)^x=e^a[/itex]
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