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Multivariable limit help

  1. Jun 26, 2009 #1
    I've been stuck on this problem for quite a while now and could use some assistance:

    Find the limit (or prove that it does not exist):

    lim{(x,y)->(1^+,oo)} x^(-y)


    I've tried switching to polar and end up with y=rsin(@) implying r diverges, which implies cos(@) must tend to zero for x to approach 1, but I'm not certain this actually proves or disproves anything. Honestly, any help would be much appreciated.
     
  2. jcsd
  3. Jun 26, 2009 #2

    Dick

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    Try some examples. Take xn=(1+1/n) and yn=n and let n go to infinity. Then xn->1+ and yn->infinity. What's the limit of xn^(-yn)? Then try xn=(1+2/n). Conclusion?
     
  4. Jun 26, 2009 #3
    Why didn't I think of that? 1/e, 1/e^2, 1/e^3...

    Lol, thanks.
     
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