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## Main Question or Discussion Point

Long story short, I said on an exam that...

1/(1+e^-(x)) =~(is nearly equal to) 1-e^-(x); note* x > 50 , they are also inversely proportional when x<-50 but that isnt specific to the problem

I used this to prove a theorem regarding hole density in semiconductors ""when x is very very large""...It was marked incorrectly but the question stated that the magnitude of x would be >50. I noticed the limiting behavior of this as it goes from 50 to infinity and they appear to be equal, especially when approximations are made in the 'books proof' to simplify the equation, mainly throwing low integers away that do not effect a number of much higher magnitude.

If I made a correct approximation and still obtained the same result equation, just because I did it differently shouldn't make it incorrect, would anyone agree?

1/(1+e^-(x)) =~(is nearly equal to) 1-e^-(x); note* x > 50 , they are also inversely proportional when x<-50 but that isnt specific to the problem

I used this to prove a theorem regarding hole density in semiconductors ""when x is very very large""...It was marked incorrectly but the question stated that the magnitude of x would be >50. I noticed the limiting behavior of this as it goes from 50 to infinity and they appear to be equal, especially when approximations are made in the 'books proof' to simplify the equation, mainly throwing low integers away that do not effect a number of much higher magnitude.

If I made a correct approximation and still obtained the same result equation, just because I did it differently shouldn't make it incorrect, would anyone agree?