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Math Help - asymptotic relations

  1. #1
    tur
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    asymptotic relations

    the problem goes like that:

    show that if f(x)-g(x)<<1 (x->0+), then exp(f(x))~exp(g(x)) (x->infinity)

    thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by tur View Post
    the problem goes like that:

    show that if f(x)-g(x)<<1 (x->0+), then exp(f(x))~exp(g(x)) (x->infinity)

    thanks
    You will have to be more precise about what:

    "f(x)-g(x)<<1"

    (It seems likely that you mean "|f(x)-g(x)|<<1" that is the difference is close to zero, rather than "f(x)-g(x)" is of large absolute value and negative.)

    and

    " ~ "

    means, what happens is that:

    \frac{\exp(f(x))}{\exp(g(x))} \to k as x \to \infty and k\approx 1 under one interpretation and k \approx 0 under another

    RonL
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