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Math Help - limits

  1. #1
    Junior Member
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    limits

    Hi!!

    I'm very confused about limits.. Can someone please correct my working out? Because I'm very sure that I'm wrong, but I don't know what to do. Thank you
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  2. #2
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    Quote Originally Posted by gconfused View Post
    Hi!!

    I'm very confused about limits.. Can someone please correct my working out? Because I'm very sure that I'm wrong, but I don't know what to do. Thank you
    the second part just becomes 1 as n->infinity.

    the first part:









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  3. #3
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    Only the last step is wrong

    lim n->oo 1/( 1+ Y/n)^n * [1 + Y/n]^-1
    = lim n->oo 1/( 1+ Y/n)^n * lim n->oo [1 + Y/n]^-1
    = 1/ e^Y * 1
    = exp(-Y)
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  4. #4
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    Thank you guys
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  5. #5
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    It's easier to see the result if you make the substitution k=\frac{y}{n} where k \to 0 when n \to \infty

    \lim_{k \to 0}(1+k)^{-y/k}=\lim_{k \to 0}e^{ln{(1+k)^{-y/k}}}=\lim_{k \to 0}e^{-y \cdot \frac{ln(1+k)}{k}}=e^{-y}
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