Alv95
- 20
- 0
I have some problems finding Taylor's expansion at infinity of
<br /> f(x) = \frac{x}{1+e^{\frac{1}{x}}} <br />
I tried to find Taylor's expansion at 0 of :
<br /> g(u) = \frac{1}{u} \cdot \frac{1}{1+e^u} \hspace{10 mm} \mbox{ where } \hspace{10 mm} u = 1/x <br />
in order to then use the known expansion of \frac{1}{1+t} but the problem is that I can not do it because :
\lim_{ u \to 0 } e^{u} = 1 \hspace{10 mm} \mbox{ and not } 0Any ideas on how to do it?
Thanks 
<br /> f(x) = \frac{x}{1+e^{\frac{1}{x}}} <br />
I tried to find Taylor's expansion at 0 of :
<br /> g(u) = \frac{1}{u} \cdot \frac{1}{1+e^u} \hspace{10 mm} \mbox{ where } \hspace{10 mm} u = 1/x <br />
in order to then use the known expansion of \frac{1}{1+t} but the problem is that I can not do it because :
\lim_{ u \to 0 } e^{u} = 1 \hspace{10 mm} \mbox{ and not } 0Any ideas on how to do it?

