/sci/ - Science & Math

<div class="math">
x \log(1+\frac 1 x) = x\log(\frac{x+1}{x}) = \log(\frac{(1+x)^x}{x^x}) </div>

Er.

math]\bf{4}\mathbb{CHAN~}\bf{/}\mathbb{SCI}\bf{/}\mathbb{~RULES:}[/math]
<span class="math">\bf{1}\Rightarrow \bf{All~science~and~math~related~topics~welcome.}[/spoiler]
<span class="math">\bf{2}\Rightarrow \bf{Homework~threads~will~be~deleted,~and~the~poster~banned.}[/spoiler]
<span class="math">\bf{3}\Rightarrow \bf{No~"religion~vs.~science"~threads.}[/spoiler]

<span class="math">\bf{4}\mathbb{CHAN~}\bf{/}\mathbb{SCI}\bf{/}\mathbb{~RULES:}[/spoiler]
<span class="math">\bf{1}\Rightarrow \bf{All~science~and~math~related~topics~welcome.}[/spoiler]
<span class="math">\bf{2}\Rightarrow \bf{Homework~threads~will~be~deleted,~and~the~poster~banned.}[/spoiler]
<span class="math">\bf{3}\Rightarrow \bf{No~"religion~vs.~science"~threads.}[/spoiler]

>>3026248
<span class="math"> \bf{4}\Rightarrow \bf{No~"retards~who~use~latex~incorrectly} [/spoiler]

use l'opital's rule:
d/dx(x/log(x/x+1)=1/(x+1/x)
=x/x+1
=1-(1/x+1)
the limit of this is 1.

>>3026252
don't be a dick

>>3026221
Maclaurin expansion of the logarithm looks like a good avenue to explore.

>>3026255
SEEING THINGS, EK? HAHAHAHAHAH

>>3026266
fuck you! you know what you did!

change x*log(1+1/x) to the following: log(1+1/x)/(x^-1)

now when you take the limit it becomes 0/0, and l'hopital's rule is applicable.

thanks

>>3026283
are these supposed to be reaction images because that's just terrible.