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