$${\frac{\left({\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{x}}}}\right)}{\mathtt{\,-\,}}{\mathtt{e}}\right)}{{\mathtt{x}}}}$$Programmer

Guest Jun 22, 2015

#2**+5 **

Thank you Alan,

How did you do the initial expansion? What kind of an expansion is that?

Melody
Jun 22, 2015

#4**0 **

Thanks Alan but worry too much, I don't understand expansions much. :(

I only know the binomial expansion.

I just wondered :/

Melody
Jun 22, 2015

#6**0 **

Thanks Alan,

I can follow most of that but you lost me at $$O(x^2)$$ and what happened to all the other powers of x?

Only answer is you feel enthused because this stuff is really over my head. I couldn't reproduce it. :(

Melody
Jun 22, 2015

#7**+5 **

Rather than writing all the other terms involving x^{2}, x^{3} etc. I've written O(x^{2}), meaning terms of order x^{2} and smaller ("smaller" because we are going to make x go to 0, so x^{4}, x^{3} etc. are going to be smaller than x^{2}). The important thing is that all these other terms will be multiples of x^{n}, where n>1, so that when they are divided by x they are still mutiples of powers of x and hence vanish in the limit as x tends to 0.

.

Alan
Jun 22, 2015