# Thread: asymptotic relations

1. ## 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

2. Originally Posted by tur
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